Solve ∫ _{-pi/4}^frac{pi{4}}dt

$$\int _ { - \frac { \pi } { 4 } } ^ { \frac { \pi } { 4 } } d t$$

Evaluate

$$\frac{\pi }{2}\approx 1.570796327$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 1\mathrm{d}t$$

Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}t=at.

$$t$$

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.

$$\frac{\pi }{4}+\frac{\pi }{4}$$

Simplify.

$$\frac{\pi }{2}$$