Q. 61 - Calculus

Question

Use the Fundamental Theorem of Calculus to find the exact

values of each of the definite integrals in Exercises $19–64$. Use

a graph to check your answer.

${\int }_{-2}^4\left|2x^2-5x-3\right|dx$

Step-by-Step Solution

Answer

The value of integral is $\frac{343}{12}$ and the plot is

Step 1. Given information

An expression is given as ${\int }_{-2}^4\left|2x^2-5x-3\right|dx$

Step 2. Evaluating integral

The plot is 

Simplify the integral as,

$$\begin{gathered} {\int }_{-2}^4\left|2x^2-5x-3\right|dx \\ ={\int }_{-2}^{-0.5}-2x^2+5x+3dx+{\int }_{-05}^{1}2x^2-5x-3dx+{\int }_1^3-2x^2+5x+3dx+{\int }_{-0.5}^{1}2x^2-5x-3dx \\ =\frac{343}{12} \end{gathered}$$