Solve ∫ (from 2 to 3) of (82^3+32-1)d2=

$$\int _ { 2 } ^ { 3 } ( 82 ^ { 3 } + 32 - 1 ) d 2 =$$

Evaluate

$$551399d_{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \left(82^{3}+32-1\right)d_{2}\mathrm{d}x$$

Find the integral of \left(82^{3}+32-1\right)d_{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(82^{3}+32-1\right)d_{2}x$$

Simplify.

$$551399d_{2}x$$

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.

$$551399d_{2}\times 3-551399d_{2}\times 2$$

Simplify.

$$551399d_{2}$$

Differentiate w.r.t. d_2

$$551399$$