Solve ∫ (from 1 to 2) of sin(θ)dθ

$$\int_{ 1 }^{ 2 } \sin ( \theta ) d \theta$$

Evaluate

$$2\sin(\frac{1}{2})\sin(\frac{3}{2})\approx 0.956449142$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \sin(\theta )\mathrm{d}\theta$$

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

$$-\cos(\theta )$$

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.

$$-\cos(2)+\cos(1)$$

Simplify.

$$2\sin(\frac{3}{2})\sin(\frac{1}{2})$$