Question #9387b

1 Answer
May 22, 2016

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.