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Section6_R - Section 6.R Review exercises 1.A 2.A A cars...

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(3/20/08) Section 6.R Review exercises 1. A A car’s velocity on a straight road at time t (hours) is 60 miles per hour for 1 < t < 4 and 75 miles per hour for 4 < t < 6. How far does it travel for 1 t 6? 2. A What is f (5) if y = f ( x ) is continuous on [ - 5 , 5], f ( - 5) = - 10, and r = f prime ( x ) is a step function with f prime ( x ) = 4 for - 5 < x < 0, and f prime ( x ) = 6 for 0 < x < 5? Express the sums in Exercises 3 and 4 with summation notation. 3. A 1 + 1 10 + ( 1 10 ) 2 + ( 1 10 ) 3 + ( 1 10 ) 4 + ( 1 10 ) 5 + ( 1 10 ) 6 4. A x 5 + x 6 + x 7 + x 8 + · · · + x 100 5. A Use the formula for the area of a trapezoid to find the value of integraldisplay 5 0 (2 x + 5) dx . 6. A Use the formula for the area of a circle to evaluate integraldisplay 3 - 3 radicalbig 9 - x 2 dx . 7. A Use areas to evaluate integraldisplay 20 0 g ( x ) dx where g ( x ) = braceleftBig x for 0 < x < 10 10 for 10 < x < 20 . 8. A Calculate directly, without using Riemann sum program, the right Riemann sum for integraldisplay 1 0 x dx corresponding to the partition 0 < 1 4 < 1 2 < 3 4 < 1. C 9. A Use a Riemann sum program to calculate the right Riemann sum for integraldisplay 2 - 2 (5 - x 2 ) dx corresponding to the partition of [ - 2 , 2] into six equal subintervals. Draw the graph of the function
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