Problem

Show that $ \displaystyle \int_0^\infty x^2 e^{-x…

03:48

Problem 76 Hard Difficulty

If $ \displaystyle \int_{-\infty}^\infty f(x)\ dx $ is convergent and $ a $ and $ b $ are real numbers, show that
$$ \int_{-\infty}^a f(x)\ dx + \int_a^\infty f(x)\ dx = \int_{-\infty}^b f(x)\ dx + \int_b^\infty f(x)\ dx $$

Answer

$\int_{0}^{\infty} f(x) d x$

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Discussion

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Watch More Solved Questions in Chapter 7

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Video Transcript

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WZ

Wen Z.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Joseph L.

Boston College