Your last submission is used for your score. LARCALC11 4.1.007.MI. –/1 points 1. My Notes Ask Your Teacher Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.) dy dt = 63t 8 y= 2. LARCALC11 4.1.011. –/4 points My Notes Ask Your Teacher Complete the table. (Use C for the constant of integration.) Original Integral 8 3. x dx Rewrite Integrate dx x x Simplify +C LARCALC11 4.1.013. –/4 points My Notes Complete the table to find the indefinite integral. (Use C for the constant of integration.) Original Integral 1 x 6 x dx Rewrite x Integrate dx x Simplify +C Ask Your Teacher 4. LARCALC11 4.1.016. –/1 points My Notes Ask Your Teacher Find the indefinite integral and check your result by differentiation. (Use C for the constant of integration.) 5. LARCALC11 4.1.019. –/1 points My Notes Ask Your Teacher Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) x3/2 + 4x + 3 6. dx LARCALC11 4.1.023. –/1 points My Notes Ask Your Teacher Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) 1 x5 dx 7. LARCALC11 4.1.025. –/1 points My Notes Ask Your Teacher Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) x +8 x 8. –/1 points dx LARCALC11 4.1.029. My Notes Ask Your Teacher My Notes Ask Your Teacher Find the indefinite integral. (Use C for the constant of integration.) (8 cos x + 9 sin x) dx 9. –/1 points LARCALC11 4.1.033. Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) 5 (sec(θ))2 − 4 sin(θ) dθ 10. LARCALC11 4.1.040.MI. –/1 points My Notes Ask Your Teacher Find the particular solution of the differential equation that satisfies the initial condition(s). f '(s) = 10s − 12s3, f(3) = 1 f(s) = 11. LARCALC11 4.1.057. –/1 points My Notes Ask Your Teacher Assume the acceleration of the object is a(t) = −32 feet per second per second. (Neglect air resistance.) A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 81 feet per second. How high will the ball go? (Round your answer to two decimal places.) ft 12. –/2 points LARCALC11 4.1.059. My Notes Ask Your Teacher Assume the acceleration of the object is a(t) = −32 feet per second per second. (Neglect air resistance.) A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 64 feet above the ground. (a) How many seconds after its release will the bag strike the ground? (Round your answer to two decimal places.) t = sec (b) At what velocity will it strike the ground? (Round your answer to three decimal places.) v = ft/sec 13. LARCALC11 4.2.005.MI. –/1 points My Notes Ask Your Teacher Find the sum by adding each term together. Use the summation capabilities of a graphing utility to verify your result. 6 (8i + 9) i=1 14. LARCALC11 4.2.007. –/1 points My Notes Ask Your Teacher Find the sum by adding each term together. Use the summation capabilities of a graphing utility to verify your result. (Round your answer to four decimal places.) 7 k =3 15. 1 2 k +8 LARCALC11 4.2.009. –/1 points My Notes Ask Your Teacher Find the sum by adding each term together. Use the summation capabilities of a graphing utility to verify your result. 8 k =0 c 16. LARCALC11 4.2.017. –/1 points My Notes Ask Your Teacher Use the properties of summation and the Summation Formulas Theorem to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. 10 3 i=1 17. LARCALC11 4.2.021. –/1 points My Notes Ask Your Teacher Use the properties of summation and the Summation Formulas Theorem to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. 16 (i − 1)2 i=1 18. –/1 points LARCALC11 4.2.023. My Notes Ask Your Teacher Use the properties of summation and the Summation Formulas Theorem to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. 8 i=1 i(i + 9)2 19. LARCALC11 4.2.025.MI. –/5 points My Notes Ask Your Teacher My Notes Ask Your Teacher Use the summation formulas to rewrite the expression without the summation notation. n 8i + 5 i=1 n2 S(n) = Use the result to find the sums for n = 10, 100, 1000, and 10,000. n= 10 n = 100 n = 1,000 n =10,000 20. LARCALC11 4.2.029.MI. –/2 points Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 3, [0, 2], 4 rectangles < Area < 21. –/2 points LARCALC11 4.2.031. My Notes Ask Your Teacher Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. g(x) = 2x2 − x − 1, [3, 5], 4 rectangles < Area < 22. –/2 points LARCALC11 4.2.037. My Notes Ask Your Teacher Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y= 3x upper sum lower sum 23. –/2 points LARCALC11 4.2.039. My Notes Ask Your Teacher Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y= upper sum lower sum 7 x 24. –/2 points LARCALC11 4.2.042. My Notes Ask Your Teacher Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function f(x) = 8 − 2x lower sum s(n) = upper sum S(n) = 25. –/1 points Interval [1, 2] LARCALC11 4.3.005.MI. My Notes Ask Your Teacher My Notes Ask Your Teacher Evaluate the definite integral by the limit definition. 6 8 dx 1 26. –/1 points LARCALC11 4.3.009. Evaluate the definite integral by the limit definition. 3 2 (x2 + 2) dx LARCALC11 4.3.011. –/2 points 27. My Notes Ask Your Teacher Write the limit as a definite integral on the interval [a, b], where c i is any point in the ith subinterval. Limit lim ||Δ|| → 0 Interval n (6c i + 2) Δxi [−1, 8] i=1 dx -1 –/2 points 28. LARCALC11 4.3.015. My Notes Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 4 − |x| dx -2 Ask Your Teacher –/2 points 29. LARCALC11 4.3.019. My Notes Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = cos(x) dx 0 Ask Your Teacher 30. –/2 points LARCALC11 4.3.023. Sketch the region whose area is given by the definite integral. 8 0 7 dx Use a geometric formula to evaluate the integral. My Notes Ask Your Teacher 31. –/2 points LARCALC11 4.3.027. Sketch the region whose area is given by the definite integral. 2 0 (2x + 4) dx Use a geometric formula to evaluate the integral. My Notes Ask Your Teacher 32. LARCALC11 4.3.039.MI. –/1 points My Notes Ask Your Teacher My Notes Ask Your Teacher Evaluate the integral using the following values. 6 2 6 6 x3 dx = 320, 6 x dx = 16, 2 dx = 4 2 (2x3 − 12x + 7) dx 2 33. LARCALC11 4.3.042.MI. –/4 points 3 Given 0 f(x) dx = 6 and 6 3 6 (a) f(x) dx 0 3 (b) f(x) dx 6 3 (c) f(x) dx 3 6 (d) 3 −5f(x) dx f(x) dx = −3 , evaluate the following. 34. LARCALC11 4.3.045. –/2 points Use the table of values to find lower and upper estimates of 10 0 f(x) dx. Assume that f is a decreasing function. lower estimate upper estimate x 0 2 4 6 8 10 f(x) 29 24 4 −6 −22 −30 My Notes Ask Your Teacher 35. LARCALC11 4.3.047. –/6 points My Notes Ask Your Teacher The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas. 2 (a) f(x) dx 0 6 (b) f(x) dx 2 (c) 2 −4 (d) 6 −4 (e) f(x) dx f(x) dx 6 −4 |f(x)| dx (f) 6 [f(x) + 2] dx −4 Submit Assignment Home Save Assignment Progress My Assignments Copyright Request Extension 2020 Cengage Learning, Inc. All Rights Reserved luede.yang@yahoo.com (sign out) Home My Assignments Grades Communication Calendar My eBooks MA30220200101204, section 1204, Spring 2020 INSTRUCTOR Grantham University Week 7 Quiz (MA302) (Quiz) Grantham University, KS Current Score QUESTION 1 2 3 4 5 6 7 8 9 10 POINTS –/5 –/5 –/5 –/5 –/5 –/5 –/5 –/5 –/5 –/5 Due Date TUE, FEB 25, 2020 11:59 PM CST Request Extension Assignment Submission & Scoring Assignment Submission TOTAL SCORE –/50 0.0% For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. –/5 points LarCalc11 4.1.019. My Notes Ask Your Teacher Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) x3/2 + 4x + 2 2. –/5 points dx LarCalc11 4.1.029. My Notes Ask Your Teacher My Notes Ask Your Teacher Find the indefinite integral. (Use C for the constant of integration.) (8 cos x + 9 sin x) dx 3. –/5 points LarCalc11 4.1.040.MI. Find the particular solution of the differential equation that satisfies the initial condition(s). f '(s) = 10s − 12s3, f(s) = f(3) = 1 4. –/5 points LarCalc11 4.2.007. My Notes Ask Your Teacher Find the sum by adding each term together. Use the summation capabilities of a graphing utility to verify your result. (Round your answer to four decimal places.) 8 1 k =4 5. –/5 points k2 + 8 LarCalc11 4.2.029.MI. My Notes Ask Your Teacher Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 3, [0, 2], 4 rectangles < Area < 6. –/5 points LarCalc11 4.2.042. My Notes Ask Your Teacher Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function f(x) = 9 − 2x lower sum s(n) = upper sum S(n) = Interval [1, 2] –/5 points 7. LarCalc11 4.3.015. My Notes Ask Your Teacher Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 4 − |x| dx -2 8. –/5 points LarCalc11 4.3.023. Sketch the region whose area is given by the definite integral. 8 0 5 dx Use a geometric formula to evaluate the integral. My Notes Ask Your Teacher LarCalc11 4.3.039.MI. –/5 points 9. My Notes Ask Your Teacher My Notes Ask Your Teacher Evaluate the integral using the following values. 6 6 x3 dx = 320, 2 6 6 x dx = 16, 2 dx = 4 2 (2x3 − 10x + 9) dx 2 10. LarCalc11 4.3.042.MI. –/5 points 3 Given 0 f(x) dx = 8 and 6 3 f(x) dx = −5 , evaluate the following. 6 (a) f(x) dx 0 3 (b) f(x) dx 6 3 (c) 3 f(x) dx 6 (d) −5f(x) dx 3 Submit Assignment Home Save Assignment Progress My Assignments Request Extension Copyright 2020 Cengage Learning, Inc. 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