UMUC MATH, FALL 2016 QUIZ 3 KOBI SNITZ (1) Let g(x) = x1 , consider the integral Z g(x) dx 1 Does this integral converge ? If it does, to what value and if it does not show why. (2) Consider the same function g(x) = x1 and the same limit of integration but this time consider the volume of solid created by revolving the graph of g around the x-axis. Does the integral of the volume diverge ? If so show why. If the integral converges, to what value. Does your answer to this question contradicts the answer to question 1. (3) consider the integral Z 1 dx. 3+ 1 x 10 x Does this integral converge or diverge ? explain why. (4) find the anti derivative of Z 1 dx x2 4x + 5 1