Solve ∫ (from 0 to 1) of pix^4 wrt x

$$\int_{ 0 }^{ 1 } \pi { x }^{ 4 } d x$$

Evaluate

$$\frac{\pi }{5}\approx 0.628318531$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \pi x^{4}\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\pi \int x^{4}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{4}\mathrm{d}x with \frac{x^{5}}{5}.

$$\pi \times \frac{x^{5}}{5}$$

Simplify.

$$\frac{\pi x^{5}}{5}$$

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.

$$\frac{1}{5}\pi \times 1^{5}-\frac{1}{5}\pi \times 0^{5}$$

Simplify.

$$\frac{\pi }{5}$$