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1 Practice Exam # (.95.5) (696850) Due: Tue May :0 AM PDT Question Question Details SCalcET [ ] A particle is moving with the given data. Find the position of the particle. a(t) = t 7t + 5, s(0) = 0, s(1) = 0 s(t) =

2 . Question Details SCalcET [508] (a) Estimate the area under the graph of R 3 = 3 f(x) = 1 + x from x = 1 to x = using three rectangles and right endpoints. Then improve your estimate by using six rectangles. R 6 = 18.5 Sketch the curve and the approximating rectangles for R 3.

3 Sketch the curve and the approximating rectangles for R 6.

4 (b) Repeat part (a) using left endpoints. L 3 = 11 L 6 = 1.5 Sketch the curve and the approximating rectangles for L 3.

5 Sketch the curve and the approximating rectangles for L 6.

6 (c) Repeat part (a) using midpoints. M 3 = 1 M 6 = 1.75 Sketch the curve and the approximating rectangles for M 3.

7 Sketch the curve and the approximating rectangles for M 6.

8 (d) From your sketches in parts (a)(c), which appears to be the best estimate? M 6 R 6 L 6 3. Question Details SCalcET [15355] (a) Find an approximation to the integral (x 10x) dx using a Riemann sum with right endpoints and n = 8. R 8 = (b) If f is integrable on [a, b], then evaluate (x 10x) dx. 5/3 b f(x) dx n b a = lim f(x i ) Δx, where Δx = and x i = a + i Δx. n n i = 1 Use this to

9 . Question Details SCalcET MI. [191810] The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. (a) 10 g(x) dx (b) 30 g(x) dx 10 (c) 35 g(x) dx 5. Question Details SCalcET [ ] Evaluate the integral by interpreting it in terms of areas x dx

10 0 6. Question Details SCalcET MI. [153597] Write as a single integral in the form b f(x) dx. f(x) dx 1 5 f(x) dx 5 + f(x) dx 1 f(x) dx 7. Question Details SCalcET [177636] Each of the regions A, B, and C bounded by the graph of f and the xaxis has area 3. Find the value of [f(x) + x + 3] dx. 3 I = [f(x) + x + 3] dx = f(x) dx + x dx + 3 dx = I 1 + I + I 3 I 1 = 3 [area below xaxis] = I = ()() [area of triangle, see figure] + ()() = 8 + = 6 I 3 = 3 [ ( )] = 3(6) = 18 Thus, I = 3 + ( 6) + 18 = 3.

11 1 8. Question Details SCalcET [ ] If m f(x) M for a x b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b a) b f(x) dx M(b a). Use this property to estimate the value of the integral. 6 3xe x dx (smaller value) (larger value) 9. Question Details SCalcET XP. [183580] Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(y) = y t sin 5t dt g '(y) = 10. Question Details SCalcET XP. [177091] Evaluate the integral. 9 t (1 + t) dt

12 11. Question Details SCalcET XP. [17763] Evaluate the integral. 16 3x 8 x dx 1. Question Details SCalcET [186568] Evaluate the definite integral. 1/x e dx x Question Details SCalcET [ ] Evaluate the definite integral. π/10 cos 5x sin(sin 5x) dx 1. Question Details SCalcET [ ] Evaluate the definite integral. 9 dx 3 (7 + x)

13 3 15. Question Details SCalcET [18657] Evaluate the definite integral. e 16 e 6 x dx ln x 16. Question Details SCalcET [ ] Evaluate the definite integral. 1 e z + 7 e z + 7z dz 17. Question Details SCalcET [ ] The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t t, 1 t 7 (a) Find the displacement. 78 m (b) Find the distance traveled by the particle during the given time interval. 66/3 m Assignment Details Name (AID): Practice Exam # (.95.5) (696850) Submissions Allowed: 100 Category: Homework Code: Locked: Yes Author: Mkrtchyan, Tigran ( mkrtcht@lamission.edu ) Last Saved: May 5, :3 PM PDT Permission: Protected Randomization: Person Which graded: Last Feedback Settings Before due date Question Score Assignment Score Publish Essay Scores Question Part Score Mark Add Practice Button Help/Hints Response Save Work After due date Question Score Assignment Score

14 Publish Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response

4/16/2015 Assignment Previewer

4/16/2015 Assignment Previewer Practice Exam # 3 (3.10 4.7) (5680271) Due: Thu Apr 23 2015 11:59 PM PDT Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1. Question Details SCalcET7 3.11.023. [1644808] Use the definitions