Solve ∫ _{-pi/4}^frac{3pi{4}}sin(x) wrt x

$$\int_{ - \frac{ \pi }{ 4 } }^{ \frac{ 3 \pi }{ 4 } } \sin ( x ) d x$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

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.

$$-\cos(\frac{1}{4}\times 3\pi )+\cos(-\frac{1}{4}\pi )$$

Simplify.

$$\sqrt{2}$$