Unit Six AP Calculus Unit 6 Review Definite Integrals. Name Period Date NONCALCULATOR SECTION


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1 Unit Six AP Clculus Unit 6 Review Definite Integrls Nme Period Dte NONCALCULATOR SECTION Voculry: Directions Define ech word nd give n exmple. 1. Definite Integrl. Men Vlue Theorem (for definite integrls) Short Answer 3. Under wht conditions re RRAM. LRAM, MRAM nd Trpezoidl method going to e under or over estimtes. Consider things like incresing nd decresing function nd concve up nd down. 4. Descrie the Fundmentl Theorem of Clculus for finding the derivtive of n integrl.. How is the re under curve relted to the definite integrl of function? Hos does the re eteen the curve nd the x xis compre to the definite integrl? Review 6. A lloon rises t the rte of 8 feet per second from point on the ground 6 feet from n oserver. Find the rte of chnge of the ngle of elevtion when the lloon is feet ove the ground.. Find vlue so tht the function 3 x, x 1 f( x) x 1, x 1 is continuous. True Flse questions worth points ech. (If flse give n exmple.) 1. Points of Inflection only occur where the second derivtive chnges from positive to negtive.. If function is integrle on n intervl if is continuous on tht intervl 3. If function is diverentile on n intervl if is continuous on tht intervl 4. Reversing the limits of n integrl will lwys produce negtive vlue.. Using trpezoidl sum to estimte the re under curve on intervl tht is concve down nd positive for ll vlues on tht intervl will underestimte the ctul re. Pge 1 of 6
2 Unit Six AP Clculus Unit 6 Review Definite Integrls 6. f(x) g(x)dx = f(x) g(x)dx where nd re constnts.. (c f(x) + d g(x))dx re constnts. = c f(x) + d g(x)dx where,, c nd d t 8. If g(x) = f(t)dt, then g (x) = xf(x ) 9. Evlute the definite integrl (leve you nswer in simplest form) : π 3 π 3 cos(x) dx 1. Evlute the definite integrl (leve you nswer in simplest form): x + 4x dx Evlute the definite integrl (leve you nswer in simplest form): e 1 1 dx x 1. Evlute the definite integrl (leve you nswer in simplest form): 4x3 4x+3 dx x 13. Evlute 6 sec x dx Pge of 6
3 Unit Six AP Clculus Unit 6 Review Definite Integrls 14. Find dy x y t t dt. dx if 3 1. Use the Trpezoidl Rule with n 4 to pproximte the re of the region in the first qudrnt enclosed y the xxis nd the grph of the function y x x Use the grph of the integrnd nd re to evlute work involved in finding the nswer. Multiple Choice Questions: Circle the est nswer. x dx. Sketch the grph nd show ll 1. Suppose tht f xdx 6 nd g x dx 1. Which of the following is not necessrily true? (A) g x dx (B) f x g x dx 16 (C) f x g x dx 6 (D) f x g x dx 4 (E) f x 3g x dx 18 Pge 3 of 6
4 Unit Six AP Clculus Unit 6 Review Definite Integrls 18. A prticle moves long coordinte xis. Its position t time t (sec) is f is the function whose grph is shown. t s t f x dx cm, where ) Wht is the prticle s position t t? ) Wht is the prticle s position t t 3? c) Wht is the prticle s velocity t t? d) Approximtely when is the ccelertion zero? e) At wht time during the first seconds does s hve its lrgest vlue? Pge 4 of 6
5 Unit Six AP Clculus Unit 6 Review Definite Integrls Nme Period Dte CALCULATOR SECTION Directions: Show ll work completed to otin your finl nswers. Prtil credit my e given for incorrect nswers. No credit my e given for prolems without work if it is required to otin the nswer. Circle or ox in your finl nswers. 19. Wht is the verge vlue of y x x 3 1 on the intervl,? Write the integrl in correct nottion used to find the verge vlue nd use your clcultor to evlute the nswer. 1. Sketch the region R enclosed etween the grph of y x 3x nd the xxis for 1 x. Prtition 1, into 4 suintervls nd show the four rectngles tht MRAM uses to pproximte the re of R. 1. Find MRAM 4 for the region descried in question 1. Show your work. You my use your clcultor for computtion only. Pge of 6
6 6 ft 118 ft 13 ft 143 ft 139 ft 136 ft 13 ft 139 ft 13 ft 1 ft 6 ft Unit Six AP Clculus Unit 6 Review Definite Integrls. A medow hs the shpe shown, where the mesurements shown were tken t 3foot intervls. Use the Trpezoidl Rule to estimte the re of the medow. (Figure not drwn to scle.) Multiple Choice Question: Circle the est nswer. 3. If k nd the re under the curve y cos x from x k to x is.1, then k? (A) 1.41 (B) (C) 1. (D) 1.1 (E).436 Pge 6 of 6
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