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# Integration Question

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For every one-dimensional set C for which the integral exists, let Q(C) = &#8747;c f(x) dx , where f(x) = 6x(1 - x) , 0 < x < 1, zero elsewhere, otherwise let Q(C) be undefined. If C1 = { x : ¼ < x < ¾ } , C2 = {1/2}, C3 = {x: 0 < x < 10}. Find Q(C1), Q(C2) and Q(C3).

Without doing any work I would think the C2 = 0. So I am concentrating on the other 2 problems. And I would also think that once I properly integrate the problem I would just plug in the numbers and get my solutions for C1 and C3.

So the problem as I see is this
&#8747; 6x(1-x) dx
= 6 &#8747;x(1 - x)dx
I would think that I would use Integration by parts.
u = x dv/dx = 1 -x
du/dx = 1 v = (x2 - 2x) / 2 ???????

Assuming the above are correct and I am not sure that they are what are the next step to solving this problem. I know from the answers in the back of the book that they should be Q(C1) = 11/16, Q(C2) = 0, Q(C3) = 1.

https://brainmass.com/math/integrals/integration-question-probability-calculus-403388