Solve ∫ (from - 2 to 1) of 5-t^2 wrt x=

$$\int _ { - 2 } ^ { 1 } 5 - t ^ { 2 } d x =$$

Evaluate

$$15-3t^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 5-t^{2}\mathrm{d}x$$

Find the integral of 5-t^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(5-t^{2}\right)x$$

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.

$$\left(5-t^{2}\right)\times 1-\left(5-t^{2}\right)\left(-2\right)$$

Simplify.

$$-3t^{2}+15$$

Differentiate w.r.t. t

$$-6t$$