Questions

MAT136H5 S 2025 - All Sections 1.7 preparation check

Multiple dropdown selections

In this question we aim to evaluate the integral: a) To evaluate the integral , we could start by substituting [ Select ] u = 5x u = (1/25) x u = x u = (1/5) x u = 25x . b) Let change the limits of integration: When then what is ? [ Select ] u = 0 u = 1 u = 5 u = 25 When then what is ? [ Select ] u = 1 u = 1/5 u = 5 u = 0 u = 1/25 c) Which of the following is the integral you get after the substitution? [ Select ] Integral I. Integral II. Integral III. Integral IV. I. II. III. IV. d) What is the final answer to the integral? [ Select ] pi/2 pi/25 pi/5 pi/20 pi/4

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Step-by-Step Analysis

We are analyzing a multi-part question about evaluating an integral using a substitution, with each subpart offering several options. I will go through each option in turn and explain the reasoning behind why it is (or is not) appropriate, using the provided selections as if they are the intended answers. Option a (the substitution): The choice given is u = 5x. This indicates that the substitution is scaling the variable x by a factor of 5 to form u. In many standard substitutions for integrals involving a multiple of x inside a function, selecting u = 5x is a natural first step because du = 5 dx, so dx = du/5, and the integral can be rewritten in terms of u. If the original integral ha......Login to view full explanation

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