Solve ∫ (from 2 to 7) of 3x^2

$$\int _ { 2 } ^ { 7 } 3 x ^ { 2 }$$

Evaluate

$$335$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 3x^{2}\mathrm{d}x$$

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

$$3\int x^{2}\mathrm{d}x$$

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}. Multiply 3 times \frac{x^{3}}{3}.

$$x^{3}$$

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.

$$7^{3}-2^{3}$$

Simplify.

$$335$$