Solve ∫ (from 0 to frac { pi) of {2}}1/2sinx wrt x

$$\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { 1 } { 2 } \sin x d x$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Evaluate the indefinite integral first.

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

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

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

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

$$-\frac{\cos(x)}{2}$$

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.

$$-\frac{1}{2}\cos(\frac{1}{2}\pi )+\frac{1}{2}\cos(0)$$

Simplify.

$$\frac{1}{2}$$