Solution Found!
If f is continuous and y 9 0 fsxd dx 4, find y 3 0 xfsx 2 d dx
Chapter 5, Problem 88(choose chapter or problem)
QUESTION:
\(\text { If } f \text { is continuous and } \int_{0}^{9} f(x) d x=4 \text {, find } \int_{0}^{3} x f\left(x^{2}\right) d x \text {. }\)
Questions & Answers
QUESTION:
\(\text { If } f \text { is continuous and } \int_{0}^{9} f(x) d x=4 \text {, find } \int_{0}^{3} x f\left(x^{2}\right) d x \text {. }\)
ANSWER:Step 1 of 2
Let: \(u=x^{2}\)
\(d u=2 x d x \Rightarrow \frac{d u}{2}=x d x\)
Now we set the new limits of integration for \(u\)
\(u=\left\{\begin{array}{ll} 9 & , \text { if } x=3 \\ 0 & , \text { if } x=0 \end{array}\right.\)