explain-why-each-of-the-following-integrals-is-improper-a-displaystyle-int_12-fracxx-1-dx-b-displays

Question

Explain why each of the following integrals is improper.

(a) $ \displaystyle \int_1^2 \frac{x}{x - 1}\ dx $
(b) $ \displaystyle \int_0^\infty \frac{1}{1 + x^3}\ dx $
(c) $ \displaystyle \int_{-\infty}^\infty x^2 e^{-x^2}\ dx $
(d) $ \displaystyle \int_0^{\frac{\pi}{4}} \cot x\ dx $

Wen Zheng · Accepted Answer

explain why each was a falling into growth is improper. So before we do this problem that record the definition of improper into girls, well functions are fives into grow off our backs. May Toby is improper. If Interpol a Toby is infinite or a fax has infinite this continue t r a to B. Now let&#x27;s do the problem. B and C Interval. It&#x27;s infinite. So they&#x27;re improper into girls. For a what axe goes to one. A function acts over X minus one Cost if infinity because two nominator cost to zero So dysfunction has infinite. Did this continue? T I want to. So it is improper, integral. And for the axe goes to zero Potanin axe goes to infinity. So the function have contended acts has infinite this continuing on their own to pile of or so it is improper integral

Problem

Which of the following integrals are improper? Wh…

Problem 1 Easy Difficulty

Explain why each of the following integrals is improper.

(a) $ \displaystyle \int_1^2 \frac{x}{x - 1}\ dx $
(b) $ \displaystyle \int_0^\infty \frac{1}{1 + x^3}\ dx $
(c) $ \displaystyle \int_{-\infty}^\infty x^2 e^{-x^2}\ dx $
(d) $ \displaystyle \int_0^{\frac{\pi}{4}} \cot x\ dx $

Answer

a. Type 2 improper integral.
b. improper integral of Type 1.
c. improper integral of Type 1.
d. Type 2 improper integral.

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Video Transcript

Calculus: Early Transcendentals

Catherine R.

Heather Z.

Kristen K.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

a. Type 2 improper integral.b. improper integral of Type 1.c. improper integral of Type 1.d. Type 2 improper integral.

Calculus: Early Transcendentals

Catherine R.

Heather Z.

Kristen K.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

Catherine R.

Heather Z.

Kristen K.

Joseph L.

a. Type 2 improper integral.
b. improper integral of Type 1.
c. improper integral of Type 1.
d. Type 2 improper integral.