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August 23, 2014

August 23, 2014

Posted by **Eric** on Wednesday, May 15, 2013 at 10:50am.

f(x)= definite integral sign where a=0 and b=x.

t^2-4/(1+(cos^2(t)) dt

what should my value for u be? is it just t. not sure how to even tackle this problem.

- calculus-extrema -
**Steve**, Wednesday, May 15, 2013 at 10:53amThe clue here is that we want to find extrema of f(x), which involves finding the derivative of f. Since f(x) is defined as an integral, we don't really have to do the integration. We just apply the rules for differentiating under the integral sign. (See wikipedia, and scroll down for some examples)

f(x) = ∫[0,x] (t^2-4)/(1+(cos^2(t)) dt

so,

df/dx = (x^2-4)/(1+cos^2 x)

So, f'=0 when x^2-4 = 0, since the bottom is never zero.

Obviously the extrema are at x=2,-2.

- calculus-extrema -
**Eric**, Wednesday, May 15, 2013 at 10:59amThank you!

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