Solve ∫ (from 4 to 8) of 5/s^2ds

$$\int _ { 4 } ^ { 8 } \frac { 5 } { s ^ { 2 } } d s$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{5}{s^{2}}\mathrm{d}s$$

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

$$5\int \frac{1}{s^{2}}\mathrm{d}s$$

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

$$-\frac{5}{s}$$

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.

$$-5\times 8^{-1}+5\times 4^{-1}$$

Simplify.

$$\frac{5}{8}$$