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Chapter 4: Q. 59 (page 373)

Use the Fundamental Theorem of Calculus to find the exact

values of each of the definite integrals in Exercises 19鈥�64. Use

a graph to check your answer.

鈭�-25|x-2|dx

Short Answer

Expert verified

The value of integral is 252and the plot is

Step by step solution

01

Step 1. Given information

An expression is given as鈭�-25|x-2|dx

02

Step 2. Evaluating integral

Simplify the integral as,

鈭�-25|x-2|dx=鈭�-222-xdx+鈭�25x-2dx=-鈭�-22xdx+2鈭�-22dx+鈭�25xdx-2鈭�25dx=-x22-22+2[x]-22+x2225-2[x]25=-42+42+2(2+2)+252-42-2[5-2]=8+212-6=8+21-122=8+92=252

And the plot for verification is

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