Calculus
10th Edition
ISBN: 9781285057095
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning

#### Videos

Question
Chapter 8.8, Problem 91E

(a)

To determine

## The explanation of the difference between the integrands ∫1∞1xdx and ∫1∞1x2dx which cause one integral to converge and other to diverge.If the integrands ∫1∞1xdx and ∫1∞1x2dx causes an integral to converge and the other to diverge. Explain the differences between the two integrands.

(b)

To determine

(c)

To determine

### To calculate: The Convergence of integrand ∫1∞sinxxdx using by parts.

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Evaluating an Improper Integral :- , Determine whether the improper integral diverges or converges. Evaluate the integral if it converges :- See the equation as attached here
a. Explain why 0 ≤ x²arctan(x) ≤ (pi*x²)/4 for all 0 ≤ x ≤ 1. b. Use the properties of the integrals to show that the value of the integral lower bound is 0, higher bound is 1 and the integral is x² arctan(x) dx lies on the interval [0,pi/12]
Topic: Improper Integrals Directions: Evaluate the integral. Prove whether it is divergent or convergent.