Solve ∫ (from a to b) of siny wrt y

$$\int _ { a } ^ { b } \sin y d y$$

Evaluate

$$\cos(a)-\cos(b)$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$-\cos(y)$$

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.

$$-\cos(b)+\cos(a)$$

Differentiate w.r.t. a

$$-\sin(a)$$