Solve ∫ (from - 1 to 2) of -2tdt

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

Evaluate

$$-3$$

Solution Steps

Evaluate the indefinite integral first.

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

Factor out the constant using \int af\left(t\right)\mathrm{d}t=a\int f\left(t\right)\mathrm{d}t.

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

Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int t\mathrm{d}t with \frac{t^{2}}{2}. Multiply -2 times \frac{t^{2}}{2}.

$$-t^{2}$$

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.

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

Simplify.

$$-3$$