Solve ∫ _{-pi/2}^frac{pi{2}}(sinx+cosx) wrt x=

$$\int _ { - \frac { \pi } { 2 } } ^ { \frac { \pi } { 2 } } ( \sin x + \cos x ) d x =$$

Evaluate

$$2$$

Solution Steps

Evaluate the indefinite integral first.

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

Integrate the sum term by term.

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

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

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

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

$$-\cos(x)+\sin(x)$$

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.

$$-\cos(\frac{1}{2}\pi )+\sin(\frac{\pi }{2})-\left(-\cos(-\frac{1}{2}\pi )+\sin(-\frac{\pi }{2})\right)$$

Simplify.

$$2$$