Solve ∫ (from 0 to 1) of pi(3x)^2 wrt x

$$\int _ { 0 } ^ { 1 } \pi ( 3 x ) ^ { 2 } d x$$

Evaluate

$$3\pi \approx 9.424777961$$

Solution Steps

Expand \left(3x\right)^{2}.

$$\int _{0}^{1}\pi \times 3^{2}x^{2}\mathrm{d}x$$

Calculate 3 to the power of 2 and get 9.

$$\int _{0}^{1}\pi \times 9x^{2}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int 9\pi x^{2}\mathrm{d}x$$

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

$$9\pi \int x^{2}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$9\pi \times \frac{x^{3}}{3}$$

Simplify.

$$3\pi x^{3}$$

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.

$$3\pi \times 1^{3}-3\pi \times 0^{3}$$

Simplify.

$$3\pi$$