integral calculus: plane areas in rectangular coordinates


by delapcsoncruz
Tags: areas, calculus, coordinates, integral, plane, rectangular
delapcsoncruz
delapcsoncruz is offline
#1
Feb28-12, 07:21 AM
P: 20
1. The problem statement, all variables and given/known data

Find the area between y= 1/(x2+1) and the x-axis, from x=0 to x=1


3. The attempt at a solution

so when x=0, y=1
and when x=1, y=1/2

next i plot the points, so the intersection of the given equation is (0,1) and (1,1/2)
Yh= Y-higher= 1/(x2+1)
Yl= Y-lower= 0
the strip is vertical, so the length (L) = (Yh-Yl) and the width (W) is dx


dA=LW
dA=(Yh-Yl)dx
dA=(1/(x2+1))dx
A=∫from 0-1 dx/(x2+1)
A=Arctan x from 0-1
A=Arctan 1 -Arctan 0
A=pi/4 sq.units


was my solution correct?
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
lanedance
lanedance is offline
#2
Feb28-12, 09:53 AM
HW Helper
P: 3,309
looks good to me
SammyS
SammyS is offline
#3
Feb28-12, 09:58 AM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,418
Quote Quote by delapcsoncruz View Post
1. The problem statement, all variables and given/known data

Find the area between y= 1/(x2+1) and the x-axis, from x=0 to x=1

3. The attempt at a solution

so when x=0, y=1
and when x=1, y=1/2

next i plot the points, so the intersection of the given equation is (0,1) and (1,1/2)
Yh= Y-higher= 1/(x2+1)
Yl= Y-lower= 0
the strip is vertical, so the length (L) = (Yh-Yl) and the width (W) is dx

dA=LW
dA=(Yh-Yl)dx
dA=(1/(x2+1))dx
A=∫from 0-1 dx/(x2+1)
A=Arctan x from 0-1
A=Arctan 1 -Arctan 0
A=pi/4 sq.units

was my solution correct?
Yes.

You went through a lot of steps to get the answer.


Register to reply

Related Discussions
Areas and Lengths in Polar Coordinates. Calculus 3 Calculus & Beyond Homework 1
Triple Integral in Rectangular Coordinates Converting to Spherical Coordinates Calculus & Beyond Homework 2
Double Integral in Rectangular Coordinates Calculus & Beyond Homework 1
Triple integral over a sphere in rectangular coordinates Calculus & Beyond Homework 5
Summation of rectangular areas (calculus) problem. Introductory Physics Homework 4