which-of-the-following-integrals-are-improper-why-a-displaystyle-int_0fracpi4-tan-x-dx-b-displaystyl

Question

Which of the following integrals are improper? Why?

(a) $ \displaystyle \int_0^{\frac{\pi}{4}} 	an x\ dx $
(b) $ \displaystyle \int_0^\pi 	an x\ dx $
(c) $ \displaystyle \int_{-1}^1 \frac{dx}{x^2 - x - 2} $
(d) $ \displaystyle \int_0^\infty e^{-x^3}\ dx $

Wen Zheng · Accepted Answer

so far, eh? Look at the graph ofthe ten and ice. First interval from zero to pie before is finite and there&#x27;s a function of ten attacks has no infinite. It is continued on the interval from their tow pilot for so it is not improper. B also look at it A graph of ten an axe Wei will find Han and pile off too. Yes, infinite. So hand and eggs has infinite is continually on this angel from there to pie. So it is improper Integral. See what axe goes to make to Juan. Denominator of dysfunction. I like square minus X minus two goes to zero. This function got to infinite. What fax goes to get you one So it is improper for the this into a wall is given it so it is improper, integral.

Problem

Find the area under the curve $ y = \frac{1}{x^3}…

Problem 2 Easy Difficulty

Which of the following integrals are improper? Why?

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

Answer

a. $[0, \pi / 4]$
b. $\lim _{a \rightarrow-\pi / 2} \int_{0}^{a} \tan x d x+\lim _{b \rightarrow+\pi / 2} \int_{b}^{\pi} \tan x d x$
c. $\lim _{a \rightarrow+(-1)} \int_{a}^{1} \frac{1}{x^{2}-x-2}$
d. $\lim _{a \rightarrow \infty} \int_{0}^{a} e^{-x^{3}} d x$

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Heather Z.

Kristen K.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 7

Video Transcript

Calculus: Early Transcendentals

Grace H.

Catherine R.

Heather Z.

Kristen K.

Integration Review - Intro

Definite vs Indefinite

a. $[0, \pi / 4]$b. $\lim _{a \rightarrow-\pi / 2} \int_{0}^{a} \tan x d x+\lim _{b \rightarrow+\pi / 2} \int_{b}^{\pi} \tan x d x$c. $\lim _{a \rightarrow+(-1)} \int_{a}^{1} \frac{1}{x^{2}-x-2}$d. $\lim _{a \rightarrow \infty} \int_{0}^{a} e^{-x^{3}} d x$

Calculus: Early Transcendentals

Grace H.

Catherine R.

Heather Z.

Kristen K.

Integration Review - Intro

Definite vs Indefinite

Grace H.

Catherine R.

Heather Z.

Kristen K.

a. $[0, \pi / 4]$
b. $\lim _{a \rightarrow-\pi / 2} \int_{0}^{a} \tan x d x+\lim _{b \rightarrow+\pi / 2} \int_{b}^{\pi} \tan x d x$
c. $\lim _{a \rightarrow+(-1)} \int_{a}^{1} \frac{1}{x^{2}-x-2}$
d. $\lim _{a \rightarrow \infty} \int_{0}^{a} e^{-x^{3}} d x$