Solve ∫ (from 0 to 1) of siny wrt y

$$\int _ { 0 } ^ { 1 } \sin y d y$$

Evaluate

$$1-\cos(1)\approx 0.459697694$$

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.

$$-\cos(1)+\cos(0)$$

Simplify.

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