Test Review - R / 3 4 sec u tan udu R 4 9 1- t t dt R 2 1 (...

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MATH 1206 Test 1 Review 1. Explain how to calculate upper and lower sums of a function f on an interval [ a,b ] using n subintervals. 2. Approximate the area under f ( x ) = | x | on the interval [ - 3 , 2] using 5 subintervals and an upper sum. Could you find the exact value of the area under f ( x ) = | x | on [ - 3 , 2]? If so, find it. 3. Express R 6 - 1 3 x 3 ln xdx as a limit of a Riemann sum where P is a partition of [ - 1 , 6]. 4. If R 2 - 2 3 f ( x ) dx = 12,and R 5 - 2 f ( x ) dx = 6 find: R 2 - 2 f ( x ) dx R 3 3 f ( x ) dx R 5 2 f ( x ) dx 5. State the fundamental theorem of calculus part 1. 6. State the fundamental theorem of calculus part 2. 7. Evaluate the following integrals:
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Unformatted text preview: R / 3 4 sec u tan udu R 4 9 1- t t dt R 2 1 ( 1 x-e-x ) dx 8. If f ( x ) = R 2-x 3 ( t 4-2 t + lnt ) dt nd f ( x ). 9. What type of integral do we need to use substitution for? Explain the steps for both indenite integrals and denite integrals. 10. Evaluate the following integrals: R tan 7 x 2 sec 2 x 2 dx R tan-1 x 1+ x 2 dx R 4 2 dx x ln x 11. If d 3 r dt 3 =-cos t and r 00 (0) = r (0) = 0 and r (0) = 1, nd r ( t )....
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Test Review - R / 3 4 sec u tan udu R 4 9 1- t t dt R 2 1 (...

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