please need help with these two integral problems

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

please need help with these two integral problems

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

\[\int\limits_{0}^{\pi/2} \sin^2x*\cos^2x\]
and \[\int\limits_{?}^{?} \sin8x * \cos5x\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

how do i do them?
in the first one just multiply and divide by 4 make it sin^2 2x then convert it using 1-cos 2x = 2sin^2 x it will become a basic integral
why by 4?
and for the second one 2Sin A cos B = Sin (A+B) + Sin (A-B)
\[\sin(x+y)=\sin(x)\cos(y)+\sin(y) \cos(x) \\ \sin(x-y)=\sin(x)\cos(y)-\sin(y)\cos(x) \\ \text{ add these identities } \sin(x+y)+\sin(x-y)=2 \sin(x) \cos(y) +0 \\ \text{ now divide by } 2 \\ \frac{\sin(x+y)+\sin(x-y)}{2}=\sin(x) \cos(y) \\ \frac{1}{2} \sin(x+y)+\frac{1}{2} \sin(x-y)=\sin(x)\cos(y)\] for the second one (Which I'm late for )
coz sin 2x = 2 sin x cos x and sin ^2 2x = 4sin^2 x cos^2 x this will replace those two terms
okay so i got sin(13)+sin(3) for the second one
so now i divide the whole thing by 2?
check this exp again sin (13) + sin (3) isn't there something missing?
oh the 1/2's right
its 'x' dear
sin (13x) + sin (3x)
x's where do they go?
got it now?
so thats the final answer?
no, now you have to integrate them wrt x
how?
oh you mean turn them to cosines
yeah
okay so it would be 13cos(13x) + 3cos(3x)
right?
you should see your notes again those 12 and 3 will be in the denom
okay fixed it so for the first one its a trig identity right?
yeah
so when its sin^2x*cos^2x you always change it to 4sin^2x*cos^2x?
yep
okay
okay so i got |dw:1433738264454:dw|
whats the next step @divu.mkr
@freckles do you know how to do the first one?
\[\int\limits _0^\frac{\pi}{2}\sin^2(x) \cos^2(x) dx \\ \int\limits_0^\frac{\pi}{2} \frac{1}{4} 4 \sin^2(x) \cos^2(x) dx \\ \frac{1}{4} \int\limits_0^\frac{\pi}{2} (2 \sin(x) \cos(x))^2 dx \\ \frac{1}{4} \int\limits_0^\frac{1}{2}( \sin(2x))^2 dx \\ \] there is an awesome idendity here you should remember for this sin things with even powers or cos with even power \[\sin^2(u)=\frac{1}{2}(1-\cos(2u)) \\ \text{ and the other one \to remember } \\ \cos^2(u)=\frac{1}{2}(1+\cos(2u))\]
\[\frac{1}{4}\int\limits_0^\frac{1}{2} \frac{1}{2}(1-\cos(2[2x])) dx\]
my god its a lot to memorize
I won't lie remembering a lot of formulas actually does kind of help :p and cuts down on time to derive other formulas(identities)
so when did you use u-substitution?
I didn't yet
cause you changed the pi/2 to 1/2
you could those on the 4x thing inside the cos thing
oh that was a type-o
oh okay so how many trig identities should i know
i mean just identities not trig
that 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
there is also methods that are useful to depending on what you are doing
like you pretty much want to remember everything you can from your algebra and trig days
calculus pretty much depends on all of that
yeah this is why i hate calculus
@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
Inspirational words needed
i just hated it cause its stressful sometimes you know
but i do enjoy working out problems and stuff
maybe it is just overwhelming I guess
you 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
I 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...
guess it just takes some time to decouple calculus from algebra and see its beauty
i remember some stuff from high school math like the trig identities and pythagoeron theorem and other stuff
yeah i guess your right just takes some time you know
I 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.
For trig, I think I remember a few trig identities and derive the rest from what I knew when I needed those identities
eventually though but long after calculus 1 I was able to recall more trig identities
for 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
i think that if i had taken calculus in high school i wouldnt be struggling so much
what about for calculus 2 and 3?
you wont be struggling as much if you memorize those few trig identities
what about in differential equations?
i 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
i hope so
`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
oh okay thank you professors/authors
well its been nice chatting with you guys but i get wake up early tomorrow for calculus class
good night and thanks for the advise
@ganeshie8 is so awesome that way
gnite have horrible calc dreams ;p
i used to have horrible math dreams
for real
lol thanks
Like 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.
lol 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
@ganeshie8 It was never relaxing for me to sleep back then.
I couldn't get the math out of my head.
there is some theory that you relax more when you dream
It is all lies.
something like... you dream only when you're in deep stage of sleep
I wonder if I was really sleep all of those times then.

Not the answer you are looking for?

Search for more explanations.

Ask your own question