Solve ∫ (from 1 to 2) of x^2/35 wrt x

$$\int _ { 1 } ^ { 2 } \frac { x ^ { 2 } } { 35 } d x$$

Evaluate

$$\frac{1}{15}\approx 0.066666667$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{x^{2}}{35}\mathrm{d}x$$

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

$$\frac{\int x^{2}\mathrm{d}x}{35}$$

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}.

$$\frac{x^{3}}{105}$$

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.

$$\frac{2^{3}}{105}-\frac{1^{3}}{105}$$

Simplify.

$$\frac{1}{15}$$