Solve ∫ (from pi / 6 to pi) of cost*d

$$\int _ { \pi / 6 } ^ { \pi } \cos t \cdot d$$

Evaluate

$$\frac{5\pi \cos(dt)}{6}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \cos(td)\mathrm{d}x$$

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

$$\cos(td)x$$

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.

$$\cos(td)\pi -\frac{1}{6}\cos(td)\pi$$

Simplify.

$$\frac{5\cos(td)\pi }{6}$$

Differentiate w.r.t. t

$$-\frac{5\pi d\sin(dt)}{6}$$