Solve ∫ (from 0 to sqrt { 2) of }(pi)^2

$$\int _ { 0 } ^ { \sqrt { 2 } } ( \pi ) ^ { 2 }$$

Evaluate

$$\sqrt{2}\pi ^{2}\approx 13.957728399$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \pi ^{2}\mathrm{d}x$$

Find the integral of \pi ^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\pi ^{2}x$$

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.

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

Simplify.

$$\pi ^{2}\sqrt{2}$$