Question

Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.

${\int }_0^6(3x+2)dx$

Short answer

The exact value of definite integral is $66$.

Step-by-step solution

Step 1. Given Information  

We are given,

${\int }_0^6(3x+2)dx$

Step 2. Finding the Integral  

The definite integral is given by,

$$\begin{gathered} {\int }_0^6(3x+2)dx={\int }_0^{6}3xdx+{\int }_0^{6}2dx \\ =3{\left(\frac{x^2}{2}\right)}_0^6+2(x{)}_0^6 \\ =3\left(\frac{1}{2}\left(6^2\right)\right)+2(6-0) \\ =54+12 \\ =66 \end{gathered}$$