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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:$$ \int_0^\infty \frac{1}{\sqrt{x} (1 + x)}\ dx = \int_0^1 \frac{1}{\sqrt{x} (1 + x)}\ dx + \int_1^\infty \frac{1}{\sqrt{x} (1 + x)}\ dx $$

$\pi$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Missouri State University

Idaho State University

Boston College

Lectures

01:11

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a. The usual way to evalua…

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03:22

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03:30

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