Question

int x^2 sin(pix) dx

Answer 1

hmm integration by parts

Answer 2

let u = x^2
du = 2xdx

dv = sin (pi x)
v = -1/pi cos(pi x)

Answer 3

then you do a second integration

Answer 4

by part

Answer 5

\[\int\limits_{}^{}x ^{2}\sin (Pix) dx\]

Answer 6

an integration within an integration.....

Answer 7

\[\frac d{dx}ab=b\frac{da}{dx}+a\frac{db}{dx}\]
Multiply both sides by \(dx\):\[d(ab)=b\,da+a\,db\]and perform the integration operation\[ab=\int b\,da+\int a\,db\]and rearranging\[\int b\,da=ab-\int a\,db\]So, from here, looking at your homework question, you need to ask yourself the question: can I use \(x^2\) or \(\sin(\pi x)\) as substitutes for \(b\) or \(da\)?

Answer 8

\[-x ^{2}/\Pi \cos (Pix)+2x/\Pi ^{2} \sin (Pix)+2/\Pi ^{3}\cos (Pix)+c\]

Answer 9

that was a long one! is it correct?

Answer 10

Good work. I got the same result :)

Answer 11

awesome!

Answer 12

\[-\frac{x ^{2}\cos \pi x}{\pi}+\frac{2x \sin \pi x}{\pi ^{2}}+\frac{2\cos \pi x}{\pi ^{3}}\]