Register to reply

Calculate double integer

by kristink08
Tags: double, integer
Share this thread:
kristink08
#1
May25-09, 03:55 PM
P: 3
This was a problem on a final test I took this april in Reykjavík University and I whould be greatful if you could help me with it.

1. The problem statement, all variables and given/known data

Let f(x,y)=2x*cos(y^4) be a function and let D be area in R^2 defined by 0≤x≤1 and x^(2/3)≤y≤1.
Calculate the double integer:
∫∫f(x,y)dA

2. Relevant equations



3. The attempt at a solution

∫dx∫2x*cos(y^4)dy
I have tried to use substitution but that doesn´t lead me anywhere.
I also tried to solve it this way...
∫dy∫2x*cos(y^4)dx which leads to...
∫dy*(x^2*cos(y^4)) and when I add in for x...
∫dy*cos(y^4) and if I use substitution now I will get...
1/4*∫cos(u)du and the final answer isn´t sufficient...
1/4*(sin(1)-sin(x^(8/3)))

I would be very greatful if you could help me...
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
Dick
#2
May25-09, 04:12 PM
Sci Advisor
HW Helper
Thanks
P: 25,246
Carefully draw a sketch of the region. Now when you integrate dx, what will be the upper and lower limits of the integration in terms of y?
kristink08
#3
May25-09, 06:00 PM
P: 3
the upper limits are 1 and lower limits are x^(2/3) in terms of y
and upper limits are 1 and lower limits are 1 in terms of x

Dick
#4
May25-09, 06:52 PM
Sci Advisor
HW Helper
Thanks
P: 25,246
Calculate double integer

That's not what my picture looks like. The integration dx goes along a horizontal line through the region. It's the part above (above being the positive y direction) the curve x^(2/3)=y. Want to try again?
kristink08
#5
May26-09, 09:20 AM
P: 3
I have no clue...:S
Dick
#6
May26-09, 09:30 AM
Sci Advisor
HW Helper
Thanks
P: 25,246
The region inside of the square 0<=x<=1 and 0<=y<=1 above the curve y=x^(2/3). Pick a value of y and draw a horizontal line. Tell me what the x value is where it crosses the region. It looks to me like it will hit the y-axis first and then the curve, right?
Random Variable
#7
May26-09, 09:45 AM
P: 116
The problem requires you to change the order of integration. The limits that are given have you integrating with respect to y first.


Register to reply

Related Discussions
Why double integral could calculate area and volume.. Calculus & Beyond Homework 2
Proof Question: Prove integer + 1/2 is not an integer Calculus & Beyond Homework 4
Prove that the inverse of an integer matrix is also an integer matrix Precalculus Mathematics Homework 7
Every integer can be written as a sum of a square and square free integer Calculus & Beyond Homework 5
Double dual/Double Transpose Question Calculus & Beyond Homework 10