Solve ∫ _{-pi/3}^frac{pi{6}}cos(x)+sin(x) wrt x

$$\int_{ - \frac{ \pi }{ 3 } }^{ \frac{ \pi }{ 6 } } \cos ( x ) + \sin ( x ) d x$$

Evaluate

$$1$$

Solution Steps

Evaluate the indefinite integral first.

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

Integrate the sum term by term.

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

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

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

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

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

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.

$$\sin(\frac{\pi }{6})-\cos(\frac{1}{6}\pi )-\left(\sin(-\frac{\pi }{3})-\cos(-\frac{1}{3}\pi )\right)$$

Simplify.

$$1$$