Solve ∫ (from 0 to 1) of t^59pit

$$\int _ { 0 } ^ { 1 } t ^ { 59 } \pi t$$

Evaluate

$$\pi t^{60}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int t^{59}\pi t\mathrm{d}x$$

Find the integral of t^{59}\pi t using the table of common integrals rule \int a\mathrm{d}x=ax.

$$t^{59}\pi tx$$

Simplify.

$$t^{60}\pi x$$

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.

$$t^{60}\pi \times 1-t^{60}\pi \times 0$$

Simplify.

$$t^{60}\pi$$

Differentiate w.r.t. t

$$60\pi t^{59}$$