Solve ∫ (from 0 to a _ { 0) of }sinθdθ

$$\int _ { 0 } ^ { a _ { 0 } } \sin \theta d \theta$$

Evaluate

$$-\cos(a_{0})+1$$

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.

$$-\cos(a_{0})+\cos(0)$$

Simplify.

$$-\cos(a_{0})+1$$

Differentiate w.r.t. a_0

$$\sin(a_{0})$$