Solve ∫ (from 1 to 3) of (6/x)^2

$$\int _ { 1 } ^ { 3 } ( \frac { 6 } { x } ) ^ { 2 }$$

Evaluate

$$24$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \left(\frac{6}{x}\right)^{2}\mathrm{d}x$$

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

$$6^{2}\int \left(\frac{1}{x}\right)^{2}\mathrm{d}x$$

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

$$6^{2}\left(-\frac{1}{x}\right)$$

Simplify.

$$-\frac{36}{x}$$

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.

$$-36\times 3^{-1}+36\times 1^{-1}$$

Simplify.

$$24$$