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HH_Sec_5_4 - Math 10B Lecture Examples Section 5.4 Theorems...

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(9/30/08) Math 10B. Lecture Examples. Section 5.4. Theorems about definite integrals Example 1 What is the integral of g from 1 to 8 if its integral from 1 to 5 is - 7 and its integral from 5 to 8 is 9? Answer: integraldisplay 8 1 g ( x ) dx = 2 Example 2 What is integraldisplay 35 - 35 [ 2p ( x ) - 3q ( x )] dx if integraldisplay 35 - 35 p ( x ) dx = 10 and integraldisplay 35 - 35 q ( x ) dx = 20 ? Answer: integraldisplay 35 - 35 [2 p ( x ) - 3 q ( x )] dx = - 40 Example 3 What is integraldisplay 0 3 Y ( x ) dx if integraldisplay 4 0 Y ( x ) dx = 10 0 and integraldisplay 3 4 Y ( x ) dx = - 25 ? Answer: integraldisplay 0 3 Y ( x ) dx = - 75 Example 4 What is integraldisplay 3 0 [ 2f ( x ) - 4g ( x )] dx if integraldisplay 3 0 f ( x ) dx = 100 and integraldisplay 3 0 g ( x ) dx = 200 ? Answer: integraldisplay 3 0 [2 f ( x ) - 4 g ( x ))] dx - 600 Example 5 Use the formulas for areas of rectangles and circles to evaluate
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