   Chapter 7.R, Problem 44E

Chapter
Section
Textbook Problem

# Evaluate the integral or show that it is divergent. ∫ 2 6 y y − 2 d y

To determine

To Find:26yy2dy

Explanation

Here the integral is improper because f(y)=yy2 has the vertical asymptote at y = 2. The infinite discontinuity occurs at the left end point of [2, 6]. So,

26yy2dy=limλ2+λ6yy2dy

Try to rewrite the integrand so that you can integrate it by using one of the known techniques of integration.

26yy2dy=limλ2+λ6y2+2y2dy=limλ2+λ6(y2)1/2dy+limλ2+λ62(y2)1/2dy

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