Solve ∫ (from 0 to frac { pi) of {2}}s

$$\int _ { 0 } ^ { \frac { \pi } { 2 } } s$$

Evaluate

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

Solution Steps

Evaluate the indefinite integral first.

$$\int s\mathrm{d}x$$

Find the integral of s using the table of common integrals rule \int a\mathrm{d}x=ax.

$$sx$$

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.

$$s\times \frac{1}{2}\pi -s\times 0$$

Simplify.

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

Differentiate w.r.t. s

$$\frac{\pi}{2} = 1.5707963267948966$$