Question

F(x) = the integral from 0 to x cos(t^2)dt. Use your calculator to find F’(1)

Answer 1

By the fundamental theorem of calculus,

$\displaystyle F(x) = \int_0^x \cos(t^2) \, dt \implies F'(x) = \cos(x^2)$

and so F'(1) = cos(1).