Explanation Theorem used: If f and g are continuous and f ( x ) ≥ g ( x ) over the interval [ a , b ] , then the area bounded by y = f ( x ) and y = g ( x ) for a ≤ x ≤ b is given exactly by A = ∫ a b [ f ( x ) − g ( x ) ] d x . Calculation: The given functions are f ( x ) = x 2 − 1 and g ( x ) = − 1 2 x − 3 . Use online graphing calculator to sketch the graph of the functions f ( x ) = x 2 − 1 and g ( x ) = − 1 2 x − 3 in the interval [ − 1 , 2 ] is as shown below in Figure 1. From Figure 1, it is observed that the function f ( x ) = x 2 − 1 is greater than g ( x ) = − 1 2 x − 3 in the interval [ − 1 , 2 ]

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Chapter 6.1, Problem 3MP

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To find: The area bounded by the graphs of the equation f(x)=x2−1 and g(x)=−12x−3 from x=−1 and x=2.

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Chapter 6.1, Problem 2MP

Chapter 6.1, Problem 4MP

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The area bounded by the graphs of the equation f ( x ) = x 2 − 1 and g ( x ) = − 1 2 x − 3 from x = − 1 and x = 2 .

Solution Summary: The author illustrates how the area bounded by the graphs of the equation f(x) is 9.75 square units.

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To find: The area bounded by the graphs of the equation f(x)=x2−1 and g(x)=−12x−3 from x=−1 and x=2.

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Chapter 6 Solutions