Solve ∫ (from 1 to 3) of +2s^2+1

$$\int _ { 1 } ^ { 3 } + 2 s ^ { 2 } + 1$$

Evaluate

$$4s^{2}+2$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2s^{2}+1\mathrm{d}x$$

Find the integral of 2s^{2}+1 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(2s^{2}+1\right)x$$

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.

$$\left(2s^{2}+1\right)\times 3-\left(2s^{2}+1\right)$$

Simplify.

$$4s^{2}+2$$

Differentiate w.r.t. s

$$8s$$