Solve ∫ (from 0 to 2) of 10tdt

$$\int _ { 0 } ^ { 2 } 10 t d t$$

Evaluate

$$20$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 10t\mathrm{d}t$$

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

$$10\int t\mathrm{d}t$$

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 10 times \frac{t^{2}}{2}.

$$5t^{2}$$

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.

$$5\times 2^{2}-5\times 0^{2}$$

Simplify.

$$20$$