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\[512\int\limits_{0}^{\pi} \cos^2t sint - \sin^3t\] im stuck at how to integrate this.

use\[u=\cos t\]and\[\sin^2t=1-\cos^2t\]

so du =-sinx

how did you get cos^2t*sint for x^2+y^2dx ?

\[-512\int\limits_{0}^{?\pi} sint dt +1024\int\limits_{0}^{\pi} \cos^2tsint\] which becomes this

yes, which you can recombine to form this\[512\int_0^\pi2\cos^2t\sin t-\sin tdt\]

so would you use u=cost and du=-sint ?

yep

or could you do \[sint(\cos^2t-1)\] which becomes \[\sin^3t\] ?

and how to you propose to integrate that?

oh yeah.haha.

\[-512\int\limits_{1}^{-1}- 2u^2du - du \] ?

i mean + du

yeah, looks good

oh wait, how did 512 get negative?

im confused because du=-sint and the sint is positive so (-1/-1) would need to be multiplied right?

yeah, but you already covered that by changing thethe signs og the terms

however the double du notation is highly unorthodox and looks screwy to me, so I'd avoid it

sorry I messed up the bounds on the last integral, they should be 0 to pi

and the answer is 1706.66666666667?

nevermind thats wrong.

its right! yay!

sweet, I just hope you find your (likely algebra-based) mistake

thats what i got to too! thanks so much!

welcome!