(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]f[/tex] is continuous and [tex]\int^{9}_{0}f(x)dx = 4[/tex], find [tex]\int^{3}_{0}xf(x^{2})dx[/tex]

2. Relevant equations

None required

3. The attempt at a solution

Don't really know where to begin, but I tried:

for [tex]\int^{3}_{0}xf(x^{2})dx[/tex]

let:

[tex]u = x^{2}[/tex]

[tex]du = 2xdx[/tex]

substitute

[tex]\int^{3}_{0}xf(x^{2})dx = \int^{9}_{0}\frac{1}{2}f(u)du

[/tex]

NOW, for [tex]\int^{9}_{0}f(x)dx = 4[/tex]

let

[tex]u = x[/tex]

[tex]du = dx[/tex]

then we have

[tex]\int^{9}_{0}f(x)dx = 4 = \int^{9}_{0}f(u)du[/tex]

so now...

[tex]\int^{9}_{0}\frac{1}{2}f(u)du = (1/2)(4) = 2[/tex]

so our result, the answer to the second integral is 2.

But i'm pretty sure i'm wrong, I didn't really know where else to go with this so that's what I tried. This question is in the "u-substitution" section of our text, so that's probably the method we use, some sort of substitution.

Any help is appreciated, thank you in advance!

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# Homework Help: Problem with Integration by substitution

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