Solve ∫ (from - 3 to 2) of 3t^2+2t^2

$$\int _ { - 3 } ^ { 2 } 3 t ^ { 2 } + 2 t ^ { 2 }$$

Evaluate

$$25t^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 3t^{2}+2t^{2}\mathrm{d}x$$

Find the integral of 3t^{2}+2t^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(3t^{2}+2t^{2}\right)x$$

Simplify.

$$5t^{2}x$$

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.

$$5t^{2}\times 2-5t^{2}\left(-3\right)$$

Simplify.

$$25t^{2}$$

Differentiate w.r.t. t

$$50t$$