Question #9387b

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Answer 1 · 2016-05-22T18:56:10

First simplify $100int_0^1x^9f(x^10)dx$ through the following substitution: $u=x^10$ , so $du=10x^9dx$ .

$100int_0^1x^9f(x^10)dx=100/10int_0^1f(x^10)10x^9dx=10int_0^1f(u)du$

Note that the bounds did change, but not noticeably, since $0^10=0$ and $1^10=1$ .

Also note that $int_0^1f(u)du=int_0^1f(x)dx$ .

So, we see the value of $"....."$ is

$"....."+100int_0^1x^9f(x^10)dx="....."+10int_0^1f(x)dx="....."+50$

I'm not really sure what the $"....."$ is supposed to stand for in the context of this problem.