If the integral of f(x) from 0 to 9 = 4 , then what is the integral of x*f(x^2) from 0 to 3 equal to?

Question

int f(x),x,0,9=4

int x*f(x^2),x,0,3=?

Answer 1

[0, 3]∫x f(x²) dx
1/2 [0, 3]∫2x f(x²) dx

Let u=x², du=2x dx. When x=0, u=0 and when x=3, u=9, so the new limits of integration are 0 and 9. Thus

1/2 [0, 9]∫f(u) du
1/2 (4)
2

Answer 2

9
integral 8x/81 dx = 4
0
3
integral 8x^3/81 dx = 2
0