MATH 0230 Final: MATH 230 m230 Final Exam 2-208
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Problem 1: evaluate the de nite integral x 1 + 3x2 dx. 0: find the value of the improper integral if it converges or show it diverges: Evaluate the inde nite integrals a)r sin3 x cos8 x dx b)r 2x. Find the length of the curve y = x. 0 x 2. (you are required to evaluate the integral you setup. ) Set up an integral representing the volume of the solid formed by rotating the region bounded by y = 3x(2 x), 0 x 2 and y = 0 about x axis. Set up the integral only, you are not required to evaluate the integral. Find the sum of the convergent series, show your reasoning: a) b) Determine the convergence or divergence of the following series, show your reasoning and state clearly the convergence or divergence test you apply. a) Determine the radius of convergence of the power series.
