Solve ∫ _{-pi/2}^frac{pi{2}}cosx wrt x

$$\int _ { - \frac { \pi } { 2 } } ^ { \frac { \pi } { 2 } } \cos x d x$$

Evaluate

$$2$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \cos(x)\mathrm{d}x$$

Use \int \cos(x)\mathrm{d}x=\sin(x) from the table of common integrals to obtain the result.

$$\sin(x)$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\sin(\frac{\pi }{2})-\sin(-\frac{\pi }{2})$$

Simplify.

$$2$$