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Numerade Educator

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Problem 88 Hard Difficulty

If $ f $ is continuous and $ \displaystyle \int^9_0 f(x) \, dx = 4 $, find $ \displaystyle \int^3_0 xf(x^2) \, dx $.

Answer

$\int_{0}^{3} x f\left(x^{2}\right) d x=2$

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Video Transcript

Okay. The first thing you know we can do is we can write the integral from 0 to 3 off of ax squared D backs. Now, we know that if we let given the fact that you is x squared, we can pull out 1/2 because it's our constant. And now we know that we can write this as 1/2 off of you from 0 to 9 and then using the fundamental theme of calculus equivalent to from nine minus half of zero, divide by two, which is equivalent did too. So we know the solution to this is indeed to and again this because off of nine miles off of zeros for it.