What is the integral from-pi/2 to pi/2 of (cos(x)-4) ?

The integral from-pi/2 to pi/2 of (cos(x)-4) is 2-4pi

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integral from-pi/2 to pi/2 of (cos(x)-4)

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 4) d x

2 - 4 π

Decimal

- 10.56637 \dots

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 4 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x - \int_{- \frac{π}{2}}^{\frac{π}{2}} 4 d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x = 2

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 d x = 4 π

= 2 - 4 π

\int_{1}^{2} \frac{1}{x ^{5} + x ^{3}} d x

\int_{\frac{π}{3}}^{x} sec^{2} (t) d t

\int_{0}^{\infty} x^{6} e^{- x} d x

\int_{0}^{\infty} cos (π) x d x

\int_{0}^{\frac{π}{4}} sin^{2} (θ) d θ

What is the integral from-pi/2 to pi/2 of (cos(x)-4) ?
The integral from-pi/2 to pi/2 of (cos(x)-4) is 2-4pi