Q. 47 - Calculus

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.

${\int }_2^4\left(x^2+1\right)dx$

Step-by-Step Solution

Answer

The exact value of definite integral  is $\frac{62}{3}$.

Step 1. Given Information

We are given,

 ${\int }_2^4\left(x^2+1\right)dx$

Step 2. Finding the Integral

The definite integral is given by,

$$\begin{gathered} {\int }_2^4\left(x^2+1\right)dx={\int }_2^4{x}^{2}dx+{\int }_2^{4}1dx \\ =\frac{1}{3}\left[4^3-2^3\right]+1[4-2] \\ =\frac{1}{3}[64-8]+2 \\ =\frac{56}{3}+2 \\ =\frac{62}{3} \end{gathered}$$