Paper Writing Services evaluate the given integral: Problem 8: Find the indefinite integrals and evaluate the definite integrals. A particular change of variable is suggested.

1: Problem 2: Find the antiderivative Problem 3: Find the surface area when the line segment A in the figure below is rotated about the lines: (a) y = 1 (b) x = -2 (a)       The line segment follows the function f (x) = x + 1. The integral for the surface area of revolution is: (a)       The line segment follows the function f (y) = y – 1. The integral for the surface area of revolution is: Problem 4: A sphere of radius 2 foot is filled with 2000 pounds of liquid. How much work is done pumping the liquid to a point 5 feet above the top of the sphere? Problem 5: Find the integral Problem 6: Find the integral Problem 7: Use the definition of an improper integral to evaluate the given integral: Problem 8: Find the indefinite integrals and evaluate the definite integrals. A particular change of variable is suggested. Problem 9: Evaluate the integral Problem 10: Evaluate the integral Problem 11: Evaluate the integral Problem 12: Show that if m and n are integers, then . (Consider m = n and m ≠ n.) Problem 13: Use derivatives to determine whether the sequence below is monotonic increasing, monotonic decreasing, or neither: Problem 14: Each special wasng of a pair of overalls removes 80% of the radioactive particles attached to the overalls. Represent, as a sequence of numbers, the percent of the original radioactive particles that remain after each wasng. Problem 15: Calculate the value of the partial sum for n = 4 and n = 5, and find a formula for sn. (The patterns may be more obvious if you do not simplify each term.) Problem 16: In the proof of the Integral Test, we derived an inequality bounding the values of the partial sums between the values of two integrals: Problem 17: Use any of the methods learned from ts MATH141 class to determine whether the given series converge or diverge. Give reasons for your answers. Problem 18: Determine whether the given series Converge Absolutely, Converge Conditionally, or Diverge, and give reasons for your conclusions. Problem 19: Find the interval of convergence for the series below. For x in the interval of convergence, find the sum of the series as a function of x. (nt: You know how to find the sum of a geometric series.) Problem 20: Represent the integral as a numerical series: Use the series representation of these functions to calculate the limits. Determine how many terms of the Taylor series for f(x) are needed to approximate f to witn the specified error on the given interval. (For each function use the center c = 0.) witn 0.001 on [-1, 4].