Question

Use part 1 of the fundamental theorem of calculus to find the derivative of the function. f(x) = 0 x 4 + sec(2t) dt hint: 0 x 4 + sec(2t) dt = − x 0 4 + sec(2t) dt

Answer 1

Terrible formatting. 0 x 4? What does that mean? - x 0 4? Nobody can read that. I can't even tell what the integral is.

Is 0 x 4 supposed to mean $\int_0^x 4 ...$?

$f(x) = \displaystyle\int_0^x (4 + \sec(2t) ) dt = F(x) - F(0),\ \text{where }F'(x) = 4 + \sec (2t) \\ \\ f'(x) = F'(x) - F'(0)\ \Rightarrow\ f'(x) = 4 + \sec(2x)$