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1 Chapter 4 Test Bank 77 Test Form A Chapter 4 Name Class Date Section. Evaluate the integral: t dt. t C (a) (b) 4 t4 C t C C t. Evaluate the integral: 5 sec x tan x dx. (a) 5 sec x tan x C (b) 5 sec x C 5sec x sec x tan x C. Evaluate the integral: x x x dx. (a) x x C (b) x C 5 sec x tan x C x x C x x x 4. Evaluate the integral: sin cos d. (a) cos C (b) cos C sin C 5. Find y fx if fx x, f0 7, and f0. (a) x 9 (b) x4 7x x 7x x 4 84x 4 cos cos sin cos 6. Use at feet per second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 96 feet per second. How high will the ball go? (a) feet (b) 64 feet 4 feet 44 feet
2 78 Chapter 4 Integration 7. Use the properties of sigma notation and the summation formulas to evaluate the given sum: 0 i i. i (a) 8 (b) Let sn n Find the limit of sn as n. i i n n. 7 0 (a) (b) Let f x, x Use geometric formulas to find 6 x, x >. (a) 5 (b) 0 0. Use the Fundamental Theorem of Calculus to evaluate the integral: (a) (b) f x dx. 0 4 x dx.. Find the average value of fx x on the interval 0,. (a) (b) Evaluate the integral: x x 5 6 dx. (a) (b) 7 x 5 7 C x 5 7 C x x 4 4 5x 6 C. Evaluate the integral: x dx. 0 (a) 0 (b) x x 5 7 C
3 Chapter 4 Test Bank Evaluate the integral: cos x dx. (a) sin x C (b) sin x C sin x C sin x C 5. Evaluate the integral: x x dx. x (a) x (b) x C x C x x C 5 x x C 6. Use Simpson s Rule with n 4 to approximate (a) (b) x dx.
4 80 Chapter 4 Integration Test Form B Chapter 4 Name Class Date Section. Evaluate the integral: 5x dx. 5 (a) 5 x (b) 7 x75 C C 9x 9 C 4x 8 C. Evaluate the integral: csc x dx. (a) csc x C (b) 6 csc x cot x C csc x C. Evaluate the integral: x 4 x dx. x x x (a) x x C (b) C cot x C x C 0 4x 5x C 4. Evaluate the integral: sec tan d. tan (a) (b) sec C 4 sec4 C sec C 5. Find y fx if f x x, f0, f0. x (a) (b) x 6x 8x 6 6 x C 6 x x x 6 x x x 6 6 C 4 sec tan C 6. Use at feet per second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. For how many seconds will the ball be going upward? (a) 7 4 sec (b) 4 sec 8 sec sec
5 Chapter 4 Test Bank 8 7. Use the properties of sigma notation and the summation formulas to evaluate the given sum: 0 i i. i (a) 50 (b) Let sn n Find the limit of sn as n. i i n n. 5 7 (a) (b) Let f x, x Use geometric formulas to find 6 x, x >. (a) 8 (b) 5 0. Use the Fundamental Theorem of Calculus to evaluate the integral: 7 6 f x dx. x dx. (a) (b) x C 4. Find the average value of fx x on the interval 0,. (a) (b) 5 6. Evaluate the integral: xx 4 dx. (a) 0x x 5 (b) 0x 5 C 5x 5 C. Evaluate the integral: sin x cos x dx. (a) 8 sin4 x cos x C (b) 4 sin4 x C sin4 x C 5x x 5 C sin x cos x sin x C
6 8 Chapter 4 Integration 4. Evaluate the integral: dx. (a) (b) 0 5. Evaluate the integral: xx dx. x (a) (b) 5 x x C x C x x C 6. Use Trapezoidal Rule with n 4 to approximate x dx. (a) (b) x x C 4
7 Chapter 4 Test Bank 8 Test Form C Chapter 4 Name Class Date Section A graphing calculator is needed for some problems.. Evaluate the integral: ax b dx. ab (a) (b) a C x C a x bx C a x bx. Evaluate the integral: 4x dx. x (a) (b) x 4 C x x C 6x x C x x C. Find the particular solution of the equation fx x that satisfies the condition f 6. (a) f x 4x (b) f x 4x C f x x 6 f x x 4 4. The rate of growth of a particular population is given by dp dt 50t 00t, where P is the population size and t is the time in years. The initial population is 5,000. Use a graphing calculator to graph the population function. Then use the graph to estimate how many years it will take for the population to reach 50,000. (a) 5.7 (b) An object has a constant acceleration of 4 feet per second squared, an initial velocity of 8 feet per second, and an initial position of feet. Find the position function describing the motion of this object. (a) s 4t (b) s 4t 8t s t 5 s t 8t
8 84 Chapter 4 Integration 6. Identify the sum that does not equal the others. (a) n (b) k 5 n0 6 i i 6 k 8 j 8 j 7. Use a graphing calculator to graph fx x x 5. Then use the upper sums to approximate the area of the region between the x-axis and f on the interval 0, using 4 subintervals. (a).8 (b) fx x 8. Determine the interval(s) on which is integrable. (a) 0, 5 (b), 0 a, b, and c (e) a and c, 4 9. Use a graphing calculator as an aid in finding the area of the region above the x-axis bounded by fx 5x 5x 0. (a) 0 (b) Consider Fx t dt. Find Fx. x (a) (b) x x x x. Choose the correct quantity to fill in the blank: dx ax a 4 C. (a) ax a (b) 4ax a 4aax a. Evaluate the integral: x sec x dx. (a) 6 x sec x C (b) tan x C tan x C 5ax a 5 x tan x C
9 Chapter 4 Test Bank 85. Use a graphing calculator as an aid in finding the area in the second quadrant bounded by the x-axis and fx x x 8. 8 (a) (b) Use the general power rule to evaluate the integral: x9 5x dx. (a) (b) 5 9 5x C 0 9 5x C 9 5x C x C 5. Evaluate the integral: 5x x dx. 5 (a) x x 4 C (b) x 4 lnx C 5x 4 lnx C 0 x x 4 C
10 86 Chapter 4 Integration Test Form D Chapter 4 Name Class Date Section. Evaluate the integral: x dx.. Evaluate the integral: csc x cot x dx.. Evaluate the integral: 4. Evaluate the integral: x x dx. x cos d. sin 5. Find the function, y fx, if fx x and f. 6. Use at feet per second squared as the acceleration due to gravity. An object is thrown vertically downward from the top of a 480-foot building with an initial velocity of 64 feet per second. With what velocity does the object hit the ground? 7. Let sn n i Find the limit of sn as n. i n n. 8. Write the definite integral that represents the area of the region enclosed by y 4x x and the x-axis. 9. Evaluate: x d t 5 dt. dx 0. Use the Fundamental Theorem of Calculus to evaluate. Find the average value of fx sin x on the interval 4,.. Evaluate the integral:. Evaluate the integral: x x dx. 0 sec x dx. tan x 0 4. Evaluate the integral: x dx. t dt.
11 Chapter 4 Test Bank Evaluate the indefinite integral: x x dx. 6. Use Simpson s Rule with to approximate n 4 x dx.
12 88 Chapter 4 Integration Test Form E Chapter 4 Name Class Date Section A graphing calculator is needed for some problems.. Evaluate the integral: ax bx dx. x. Evaluate the integral: x x dx.. Find the function, y fx, if fx x and f. 4. The rate of growth of a particular population is given by dp dt 40t 70t 4, where P is the population size and t is the time in years. The initial population is 6,000. a. Determine the population function. b. Use a graphing calculator to graph the population function. Then use the graph to estimate the number of years until the population reaches 0,000. (Round your answer to one decimal place.) c. Use the population function to calculate the population after 8 years. 5. Find the limit: lim n n i i n n. x 6. Evaluate the integral: dx. 7. Use a graphing calculator to graph fx x 4 6x x 6x. Then use the upper sums to approximate the area of the region in the first quadrant bounded by f and the x-axis using 4 subintervals. (Round your answer to three decimals places.) 8. Use a graphing calculator as an aid to sketch the region whose area is indicated by the integral: x 4x 6 dx Determine if fx 5 is integrable on the interval 0,. Give a reason for your answer. x
13 Chapter 4 Test Bank Use a graphing calculator to graph fx cos x sin x. Calculate the area in the first quadrant bounded by the x-axis, the y-axis, and f. x. Consider Fx Find Fx and F. t dt. 4. Evaluate the integral:. Evaluate the integral: cos x dx. x 4 sec x dx. 4. Evaluate the integral: xx dx Consider the region bounded by the x-axis, the function fx x, x, and x. a. Use Trapezoidal Rule, with n 4, to approximate the area of the region. (Round the answer to three decimal places.) b. Use Simpson s Rule, with n 4, to approximate the area of the region. (Round the answer to three decimal places.)
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