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Chapter 4: Q. 47 (page 386)

For each pair of functions fand gand interval [a,b]in Exercises 41鈥�52, use definite integrals and the Fundamental Theorem of Calculus to find the exact area of the region between the graphs of fand gfrom x = a to x = b.

width="330" height="23" role="math">f(x)=x-1,g(x)=x2-2x-1,[a,b]=[-1,3]

Short Answer

Expert verified

The exact area is193.

Step by step solution

01

Step 1. Given Information.

The given function and interval isf(x)=x-1,g(x)=x2-2x-1,[a,b]=[-1,3].

02

Step 2. Graph of the function.

The graph of the functions is,

03

Step 3. Required area.

The exact area will be,

鈭�-13|f(x)-g(x)|dx=鈭�-10(g(x)-f(x))dx+鈭�03(f(x)-g(x))dx=鈭�-10x2-3xdx+鈭�03-x2+3xdx=x33-3x22-10+-x33+3x2203=0-(-1)33-3(-1)22+-(3)33+3(3)22-0=13+32-273+272=-263+15=193

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