Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 to x-5 of square root of Sin(t)dt.

Question

Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 to x-5 of square root of Sin(t)dt.
Please help.

drwls · Answer

I'm sorry, but the integrand "2x^2 to x-5 of square root of Sin(t)dt." does not make sense. In general, the derivative of an indefinite integral of a function is the function itself.

Nick · Answer

Ok, so if I change it to 2x^2 to x-5 of square root of Sin(x)dx, does it make sense? We haven't done any examples with an x in both the top and bottom of the integral sign. Thanks