Solve ∫ (from - 2.667 to 0.67) of 8-32^2

$$\int _ { - 2.667 } ^ { 0.67 } 8 - 32 ^ { 2 }$$

Evaluate

$$-3390.392$$

Solution Steps

Calculate 32 to the power of 2 and get 1024.

$$\int _{-2.667}^{0.67}8-1024\mathrm{d}x$$

Subtract 1024 from 8 to get -1016.

$$\int _{-2.667}^{0.67}-1016\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int -1016\mathrm{d}x$$

Find the integral of -1016 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$-1016x$$

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.

$$-1016\times 0.67+1016\left(-2.667\right)$$

Simplify.

$$-3390.392$$