QuestionEvaluate the following integral using the Fundámental Theorem of Calculus. $$\int_{-5 \pi / 2}^{5 \pi / 2}(\cos x-4) d x$$ $$\int_{-5 \pi / 2}^{5 \pi / 2}(\cos x-4) d x=\square$$ $\square$ (Type an exact answer.)

Studdy Solution
Calculate the difference $F(5\pi/2) - F(-5\pi/2)$:
$$F(5\pi/2) - F(-5\pi/2) = (1 - 10\pi) - (-1 + 10\pi)$$ $$= 1 - 10\pi + 1 - 10\pi$$ $$= 2 - 20\pi$$
The exact value of the integral is:
$$\boxed{2 - 20\pi}$$