Solve ∫ _{pi/6}^32cos(x) wrt x

$$\int_{ \frac{ \pi }{ 6 } }^{ 3 } 2 \cos ( x ) d x$$

Evaluate

$$2\sin(3)-1\approx -0.717759984$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2\cos(x)\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$2\int \cos(x)\mathrm{d}x$$

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

$$2\sin(x)$$

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.

$$2\sin(3)-2\sin(\frac{1}{6}\pi )$$

Simplify.

$$2\sin(3)-1$$