Math  /  Calculus

QuestionQuestion
Evaluate the following integral using the Fundamental Theorem of Calculus. 5π/25π/2(cosx4)dx5π/25π/2(cosx4)dx=\begin{array}{l} \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 \end{array} \square (Type an exact answer.)

Studdy Solution
Evaluate F(5π/2)F(5π/2) F(5\pi/2) - F(-5\pi/2) .
F(5π/2)F(5π/2)=(110π)(1+10π) F(5\pi/2) - F(-5\pi/2) = (1 - 10\pi) - (-1 + 10\pi)
Simplify the expression:
=110π+110π = 1 - 10\pi + 1 - 10\pi =220π = 2 - 20\pi
The exact answer is:
220π \boxed{2 - 20\pi}

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