Problem

Evaluate $$ \displaystyle \int_2^\infty \frac{1}…

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Problem 55 Hard Difficulty

The integral
$$ \int_0^\infty \frac{1}{\sqrt{x} (1 + x)}\ dx $$
is improper for two reasons: The interval $ [0, \infty) $ is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows:
$$ \int_0^\infty \frac{1}{\sqrt{x} (1 + x)}\ dx = \int_0^1 \frac{1}{\sqrt{x} (1 + x)}\ dx + \int_1^\infty \frac{1}{\sqrt{x} (1 + x)}\ dx $$

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Chapter 7

Techniques of Integration

Section 8

Improper Integrals

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Video Transcript

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Problem

Evaluate $$ \displaystyle \int_2^\infty \frac{1}…

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Related Courses

Calculus: Early Transcendentals

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Catherine Ross

Kayleah Tsai

Caleb Elmore

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Catherine Ross

Kayleah Tsai

Caleb Elmore

James StewartCalculus: Early Transcendentals

Grace He

Catherine Ross

Kayleah Tsai

Caleb Elmore

James Stewart

Calculus: Early Transcendentals