Solve ∫ _{-pi/2}^frac{pi{2}}cosvarphidvarphi

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

Evaluate

$$2$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$\sin(\phi )$$

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.

$$2$$