Solve ∫ (from 0 to pi) of acos(x) wrt x

$$\int_{ 0 }^{ \pi } a \cos ( x ) d x$$

Evaluate

$$0$$

Solution Steps

Evaluate the indefinite integral first.

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

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

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

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

$$a\sin(x)$$

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.

$$a\sin(\pi )-a\sin(0)$$

Simplify.

$$0$$

Differentiate w.r.t. a

$$0$$