Solve ∫ (from 3 pi to 4 pi) of 2sin(x) wrt x=

$$\int _ { 3 \pi } ^ { 4 \pi } 2 \sin ( x ) d x =$$

Evaluate

$$-4$$

Solution Steps

Evaluate the indefinite integral first.

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

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

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

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

$$-2\cos(x)$$

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.

$$-2\cos(4\pi )+2\cos(3\pi )$$

Simplify.

$$-4$$