Solve ∫ (from 0 to frac { pi) of {4}}sinx wrt x

$$\int _ { 0 } ^ { \frac { \pi } { 4 } } \sin x d x$$

Evaluate

$$-\frac{\sqrt{2}}{2}+1\approx 0.292893219$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$-\cos(x)$$

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.

$$-\cos(\frac{1}{4}\pi )+\cos(0)$$

Simplify.

$$-\frac{\sqrt{2}}{2}+1$$