Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Integration Worksheet - University Calculus I | MTH 1730, Study notes of Calculus

Material Type: Notes; Class: UNIVERSITY CALCULUS I; Subject: MATHEMATICS; University: St. John's University-New York; Term: Fall 2008;

Typology: Study notes

Pre 2010

Uploaded on 08/18/2009

koofers-user-2oz-1
koofers-user-2oz-1 🇺🇸

10 documents

1 / 1

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MTH 1730
Worksheet (11/20/08)
“Integration”
(1) Calculate the following integrals.
(a) Z2x5
x25xdx
(b) Z2x5
(x25x)4dx
(c) Zx(1 + 2x)dx
(d) Z1
0
exex+ 1 dx
(e) Z5
3
3x
x2dx (Use the substitution u=x2.)
(f) Zxarctan x dx (Use integration by parts.)
(2) The rate of infection of a disease (in people per month) is given by the function
I0(t) = 100t
t2+ 1, where tis the time in months since the disease broke out. Find the
total number of infected people during the first four months of the disease.
(3) Suppose the temperature in a river at a point xin meters downstream from a factory
that is discharging hot water into the river is given by T(x) = 400 0.25x2. Find
the average temperature over the interval [10,40].
(4) A region Ris enclosed by the curves y=xand y=x2. Find the area of R.
(5) Does the improper integral Z
1
6exdx converge or diverge? If it converges, what
does it converge to?

Partial preview of the text

Download Integration Worksheet - University Calculus I | MTH 1730 and more Study notes Calculus in PDF only on Docsity!

MTH 1730

Worksheet (11/20/08) “Integration”

(1) Calculate the following integrals.

(a)

∫ (^2) x − 5 x^2 − 5 x dx

(b)

∫ (^2) x − 5 (x^2 − 5 x)^4 dx

(c)

x(1 + 2x) dx

(d)

0 e

x√ex (^) + 1 dx

(e)

3

√^3 x x − 2 dx^ (Use the substitution^ u^ =^ x^ −^ 2.)

(f)

x arctan x dx (Use integration by parts.)

(2) The rate of infection of a disease (in people per month) is given by the function I′(t) = (^) t^1002 + 1t, where t is the time in months since the disease broke out. Find the total number of infected people during the first four months of the disease.

(3) Suppose the temperature in a river at a point x in meters downstream from a factory that is discharging hot water into the river is given by T (x) = 400 − 0. 25 x^2. Find the average temperature over the interval [10, 40].

(4) A region R is enclosed by the curves y = x and y = x^2. Find the area of R.

(5) Does the improper integral

1

6 e−x^ dx converge or diverge? If it converges, what does it converge to?