Solve ∫ _{t_{0}}^t2-6t

$$\int _ { t _ { 0 } } ^ { t } 2 - 6 t$$

Evaluate

$$2\left(1-3t\right)\left(t-t_{0}\right)$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2-6t\mathrm{d}x$$

Find the integral of 2-6t using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(2-6t\right)x$$

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.

$$\left(2-6t\right)t-\left(2-6t\right)t_{0}$$

Simplify.

$$2\left(1-3t\right)\left(t-t_{0}\right)$$

Differentiate w.r.t. t

$$2+6t_{0}-12t$$