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El_Arrow
 one year ago
please need help with these two integral problems
El_Arrow
 one year ago
please need help with these two integral problems

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El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\pi/2} \sin^2x*\cos^2x\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0and \[\int\limits_{?}^{?} \sin8x * \cos5x\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0@Concentrationalizing @perl @zepdrix @freckles

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in the first one just multiply and divide by 4 make it sin^2 2x then convert it using 1cos 2x = 2sin^2 x it will become a basic integral

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and for the second one 2Sin A cos B = Sin (A+B) + Sin (AB)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\sin(x+y)=\sin(x)\cos(y)+\sin(y) \cos(x) \\ \sin(xy)=\sin(x)\cos(y)\sin(y)\cos(x) \\ \text{ add these identities } \sin(x+y)+\sin(xy)=2 \sin(x) \cos(y) +0 \\ \text{ now divide by } 2 \\ \frac{\sin(x+y)+\sin(xy)}{2}=\sin(x) \cos(y) \\ \frac{1}{2} \sin(x+y)+\frac{1}{2} \sin(xy)=\sin(x)\cos(y)\] for the second one (Which I'm late for )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0coz sin 2x = 2 sin x cos x and sin ^2 2x = 4sin^2 x cos^2 x this will replace those two terms

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0okay so i got sin(13)+sin(3) for the second one

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so now i divide the whole thing by 2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0check this exp again sin (13) + sin (3) isn't there something missing?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin (13x) + sin (3x)

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0x's where do they go?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so thats the final answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, now you have to integrate them wrt x

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0oh you mean turn them to cosines

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0okay so it would be 13cos(13x) + 3cos(3x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you should see your notes again those 12 and 3 will be in the denom

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0okay fixed it so for the first one its a trig identity right?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so when its sin^2x*cos^2x you always change it to 4sin^2x*cos^2x?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0okay so i got dw:1433738264454:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0whats the next step @divu.mkr

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0@freckles do you know how to do the first one?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\int\limits _0^\frac{\pi}{2}\sin^2(x) \cos^2(x) dx \\ \int\limits_0^\frac{\pi}{2} \frac{1}{4} 4 \sin^2(x) \cos^2(x) dx \\ \frac{1}{4} \int\limits_0^\frac{\pi}{2} (2 \sin(x) \cos(x))^2 dx \\ \frac{1}{4} \int\limits_0^\frac{1}{2}( \sin(2x))^2 dx \\ \] there is an awesome idendity here you should remember for this sin things with even powers or cos with even power \[\sin^2(u)=\frac{1}{2}(1\cos(2u)) \\ \text{ and the other one \to remember } \\ \cos^2(u)=\frac{1}{2}(1+\cos(2u))\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{1}{4}\int\limits_0^\frac{1}{2} \frac{1}{2}(1\cos(2[2x])) dx\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0my god its a lot to memorize

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I won't lie remembering a lot of formulas actually does kind of help :p and cuts down on time to derive other formulas(identities)

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so when did you use usubstitution?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0cause you changed the pi/2 to 1/2

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you could those on the 4x thing inside the cos thing

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0oh okay so how many trig identities should i know

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i mean just identities not trig

freckles
 one year ago
Best ResponseYou've already chosen the best response.2that is hard to say http://www.purplemath.com/modules/idents.htm this page has a lot of useful trig identities other identities ... well I remember pascal's triangle to help expand binomials to some positive power

freckles
 one year ago
Best ResponseYou've already chosen the best response.2there is also methods that are useful to depending on what you are doing

freckles
 one year ago
Best ResponseYou've already chosen the best response.2like you pretty much want to remember everything you can from your algebra and trig days

freckles
 one year ago
Best ResponseYou've already chosen the best response.2calculus pretty much depends on all of that

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0yeah this is why i hate calculus

freckles
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 I think I seen a post you made recently about people hating math because of something or whatever is there anything you can say here to inspire @El_Arrow into loving calculus ? :p

freckles
 one year ago
Best ResponseYou've already chosen the best response.2Inspirational words needed

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i just hated it cause its stressful sometimes you know

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0but i do enjoy working out problems and stuff

freckles
 one year ago
Best ResponseYou've already chosen the best response.2maybe it is just overwhelming I guess

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you get to calculus and maybe forget a lot so you are trying to learn the calculus like things and trying to relearn everything from algebra to trig

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0I think calculus1 is simple and easy, it deals mainly with two problems : 1) slope of tangent line 2) area under curve Most of the times, it is actually the algebra/trig/geometry part (which is not calculus) that is painful and makes calculus look messy...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0guess it just takes some time to decouple calculus from algebra and see its beauty

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i remember some stuff from high school math like the trig identities and pythagoeron theorem and other stuff

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0yeah i guess your right just takes some time you know

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I think I remember learning some algebra while in calculus. I think I was also still learning algebra even after finishing calculus 1. Algebra is pretty crazy stuff.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2For trig, I think I remember a few trig identities and derive the rest from what I knew when I needed those identities

freckles
 one year ago
Best ResponseYou've already chosen the best response.2eventually though but long after calculus 1 I was able to recall more trig identities

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0for calculus1 you only need to memorize below trig identities 1) double angle identities (sin(2x), cos(2x) and tan(2x)) 2) angle sum identities (sin(a+b), cos(a+b), tan(a+b)) apart from the well known pythagorean identity sin^2x+cos^2x=1

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i think that if i had taken calculus in high school i wouldnt be struggling so much

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0what about for calculus 2 and 3?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0you wont be struggling as much if you memorize those few trig identities

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0what about in differential equations?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0i bet you felt differentiation part of calc1 easy because you know how to differentiat almost anything using product rule, quotient rule and chain rule. Integration requires "guessing", so it confuses everyone in the start... but you will get used to it after working few problems

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0`double angle` and `angle sum` are the only trig identities you will be using in most of your calc1,2,3 problems... the focus is about learning calculus, not mastering trigonometry... so professors/authors avoid problems that deal with complicated trig identities in academic courses

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0oh okay thank you professors/authors

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0well its been nice chatting with you guys but i get wake up early tomorrow for calculus class

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0good night and thanks for the advise

freckles
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 is so awesome that way

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0gnite have horrible calc dreams ;p

freckles
 one year ago
Best ResponseYou've already chosen the best response.2i used to have horrible math dreams

freckles
 one year ago
Best ResponseYou've already chosen the best response.2Like I would be dreaming about trying to solve a math problem and I would be unable to do it in my dream. I would do number crunching in my sleep. Numbers everywhere in my dreams. Math can be pretty haunting.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0lol that sounds real scary... of course there is a slight possibility that you solve one of those open hard problems in sleep and remember after waking up ;) this reminds me of benzene structure discovery :P

freckles
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 It was never relaxing for me to sleep back then.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I couldn't get the math out of my head.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0there is some theory that you relax more when you dream

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0something like... you dream only when you're in deep stage of sleep

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I wonder if I was really sleep all of those times then.
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