huffmeister (kmh4546) – HW15 – yu – (53675) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the definite integral I = Z 0 −5 2 + p 25 − x 2 dx by interpreting it in terms of known areas. 1.

huffmeister (kmh4546) – HW15 – yu – (53675) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the definite integral I = Z 0 −5 2 + p 25 − x 2 dx by interpreting it in terms of known areas. 1. I = 25π + 10 2. I = 25 4 π + 10 3. I = 25π + 5 4. I = 25 2 π + 10 5. I = 25 2 π + 5 6. I = 25 4 π + 5 002 10.0 points When f has graph R2 R1 a b c x y express the sum I = Z c a n 2f(x) − 4|f(x)| o dx in terms of the areas A1 = area(R1), A2 = area(R2) of the respective lighter shaded regions R1 and R2. 1. I = −2A1 2. I = −6A1 + 2A2 3. I = −6A1 − 2A2 4. I = 6A1 + 2A2 5. I = −6A2 6. I = 6A1 − 2A2 003 10.0 points The graph of a function f is shown in -1 0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 2 4 6 8 Compute the Riemann sum X 10 i = 1 f(x ∗ i ) ∆x when [0, 10] is subdivided into ten equal subintervals [xi−1, xi ] and x ∗ 1 = x1, x∗ 2 = x2, . . . , x∗ 10 = x10 . 1. Riemann sum = 52 huffmeister (kmh4546) – HW15 – yu – (53675) 2 2. Riemann sum = 53 3. Riemann sum = 50 4. Riemann sum = 49 5. Riemann sum = 51 004 10.0 points Below is the graph of a function f. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 2 4 6 8 −2 −4 −6 Estimate the integral I = Z 12 0 f(x) dx with six equal subintervals using right endpoints. 1. I ≈ 12 2. I ≈ 20 3. I ≈ 16 4. I ≈ 14 5. I ≈ 18 005 10.0 points If an n th-Riemann sum approximation to the definite integral I = Z b a f(x) dx is given by Xn i = 1 f(x ∗ i ) ∆xi = 5n 2 − 3n + 6 6n2 , determine the value of I. 1. I = − 1 2 2. I = 1 3. I = 4 3 4. I = 5 6 5. I = 1 3 006 10.0 points For each n the interval [2, 9] is divided into n subintervals [xi−1, xi ] of equal length ∆x, and a point x ∗ i is chosen in [xi−1, xi ]. Express the limit lim n →∞ Xn i = 1 (3x ∗ i sin x ∗ i ) ∆x as a definite integral. 1. limit = Z 2 9 3 sin x dx 2. limit = Z 2 9 3x sin x dx 3. limit = Z 9 2 3x dx 4. limit = Z 9 2 3 sin x dx 5. limit = Z 2 9 3x dx 6. limit = Z 9 2 3x sin x dx huffmeister (kmh4546) – HW15 – yu – (53675) 3 007 10.0 points Determine the definite integral I to which the Riemann sum Xn k=1 1 + k n 2 5 n converges as n → ∞. 1. I = Z 2 0 (1 + x) 2 dx 2. I = Z 2 0 (1 + x 2 ) dx 3. I = Z ∞ 0 5(1 + x) 2 dx 4. I = Z ∞ 0 (1 + x 2 ) dx 5. I = Z 1 0 5(1 + x 2 ) dx 6. I = Z 1 0 5(1 + x) 2 dx 008 10.0 points For which integral, I, is the expression 1 20 r 1 20 + r 2 20 + r 3 20 + . . . + r 20 20 ! a Riemann sum approximation? 1. I = 1 20 Z 1 0 r x 20 dx 2. I = Z 1 0 √ x dx 3. I = 1 20 Z 1 0 √ x dx 4. I = Z 1 0 r x 20 dx 5. I = 1 20 Z 20 0 √ x dx 009 10.0 points Use Riemann sums with right hand endpoints as well as the sum formula 1 2 + 22 + . . . + n 2 = 1 6 n(n + 1)(2n + 1) to determine In so that Z 1 0 (4 + x 2 ) dx = lim n→ ∞ In . 1. In = 24n 2 + (n + 1) 6n 2. In = 24n + (n + 1) n 3. In = 24n 2 + (n + 1)(2n + 1) 6n2 4. In = 24n 2 + (n + 1)(2n + 1) n2 5. In = 24n + (n + 1)(2n + 1) n2 6. In = 24n 2 + (n + 1)(2n + 1) 6n 010 10.0 points On the interval [0, 8] the continuous function f has graph -1 0 1 2 3 4 5 6 2 4 6 8 2 4 6 Determine the value of the integral I = Z 8 0 f(x) dx . huffmeister (kmh4546) – HW15 – yu – (53675) 4 1. I = 63 2 2. I = 67 2 3. I = 69 2 4. I = 65 2 5. I = 61 2 011 10.0 points Evaluate the integral I = Z 4 −4 p 16 − x2 dx by interpreting it in terms of known areas. 1. I = 24π 2. I = 16π 3. I = 40π 4. I = 32π 5. I = 8π 012 10.0 points Evaluate the integral I = Z 4 −4 1 + p 16 − x 2 dx by interpreting it in terms of known areas. 1. I = 8π + 8 2. I = 16π − 4 3. I = 8π − 4 4. I = 8π + 4 5. I = 16π + 4 6. I = 16π + 8 013 10.0 points Evaluate the integral I = Z 2 4 (3f(x) − 2g(x)) dx when Z 4 2 f(x) dx = 3 , Z 4 2 g(x) dx = 5 . 1. I = 1 2. I = 3 3. I = 4 4. I = 0 5. I = 2 014 10.0 points Continuous functions f, g are known to have the properties Z 3 1 f(x) dx = 8, Z 3 1 g(x) dx = 6 respectively. Use these to find the value of the integral I = Z 3 1 (4f(x) − g(x)) dx. 1. I = 26 2. I = 27 3. I = 23 4. I = 25 5. I = 24 huffmeister (kmh4546) – HW15 – yu – (53675) 5 015 10.0 points If f and g are continuous functions such that f(x) ≥ 0 for all x, which of the following must be true? I. Z b a f(x) g(x) dx = Z b a f(x) dx Z b a g(x) dx II. Z b a n f (x) + g(x) o dx = Z b a f(x) dx + Z b a g(x) dx III. Z b a p f(x) dx = sZ b a f(x) dx 1. I only 2. II only 3. I and II only 4. II and III only 5. III only 016 10.0 points Use properties of integrals to determine the value of I = Z 0 4 f(x) dx when Z 6 0 f(x) dx = 8, Z 6 4 f(x) dx = 6 . 1. I = −2 2. I = 14 3. I = 5 4. I = −5 5. I = −14 6. I = 2

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"