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

and \[\int\limits_{?}^{?} \sin8x * \cos5x\]

how do i do them?

why by 4?

and for the second one
2Sin A cos B = Sin (A+B) + Sin (A-B)

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|

\[\frac{1}{4}\int\limits_0^\frac{1}{2} \frac{1}{2}(1-\cos(2[2x])) dx\]

my god its a lot to memorize

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

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

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

guess it just takes some time to decouple calculus from algebra and see its beauty

yeah i guess your right just takes some time you know

eventually though but long after calculus 1 I was able to recall more trig identities

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 hope so

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

@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.