Question

Calculus Help!!
If f is continuous and ∫(upper limit:9,lower limit:0) f(x)dx=8, find ∫(upper limit:3,lower limit:0) xf(x^2)dx.

Answer 1

what should I do when they change the upper limit?

Answer 2

\[u=x^2\]

Answer 3

u = x^2
du = 2x dx --> dx = du/2x

integral 1/2 f(u) du, where limits for x are 0 to 3 but change limits for u from 0 to 9

Answer 4

I still don't really get how to change the limit!!Can you show some steps,please?

Answer 5

original limits
0 < x < 3
u = x^2
0^2 < u < 3^2
0 < u< 9

Answer 6

I got it!!Thanks a lot!!