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1. ### Area Inside Lemniscate Vector Calculus

anyone know how i can change it into a double integral to solve for the area inside the lemniscate?
2. ### Area Inside Lemniscate Vector Calculus

but i am learning about double integrals and it is only a single integration on the website link
3. ### Vector calculus double integrals

Find the volume V of the solid under the surface z=4-x^2-y^2 and over the rectangle R consisting of all points (x,y) such that 0<=x<=1 and 0<=y<=2. I have started, but am unsure if my approach is correct or not. x = 4-x^2-y^2 \int^{2}_{0}\int^{1}_{0} 4-x^{2}-y^{2} dx dy is this correct?
4. ### Area Inside Lemniscate Vector Calculus

i still need help on this, anyone have any ideas? is hanhan correct that r^2 is the area so u can integrate ??
5. ### Integration with squareroot

i'm not sure if i can use the formula to help the integration because i also have this formula somewhere, but i don't see how else i can integrate without it as the solution with the hyperbolic substitution is too difficult for me. nevermind i see how you did this, and i would have never known...
6. ### Area Inside Lemniscate Vector Calculus

i found examples in class where it is integrating the double integral w.r.t dr dtheta so do i rearrange for a to get rid of a... or do as u say and integrate w.r.t dtheta i still have not found the limits of integration yet, i dont see how i am suppose to figure all this stuff out with no...
7. ### Integration with squareroot

okay, i have read this about 10 times trying to understand this, i have tried substituting everything in to get the antiderivative you got, but i constantly get something different. why is this integral so hard , am i doing it the hard way is there an easier way to compute this.
8. ### Area Inside Lemniscate Vector Calculus

so how do i get rid of the constant?
9. ### Area Inside Lemniscate Vector Calculus

okay so i can only put it in polar coordinates, but where are the limits of integration in which i am suppose to integrate?? (r^2)^2 = 2a^2 (rcos^2theta - rsin^2theta) r r^4 = 2a^2 (rcos^2theta - rsin^2theta) r r^3 = 2a^2 (r^2cos^2theta - r^2sin^2theta) r = 2a^2 (cos^2theta - sin^2theta) r =...
10. ### Area Inside Lemniscate Vector Calculus

what does the a even mean.. my prof did not say anything about a lemniscate, I am confused out of my mind
11. ### Integration with squareroot

okay, so I have done everything and integrated the whole thing, now because I have never learnt about the hyperbolic function, i am having trouble doing this. here is my work for the rest of the integration: (previous work) integ (sqrt (1+x^2)dx) let x = sinh t dx/dt = cosh t integ...
12. ### Iterated Integrals bounded by curves

how would i know this for future reference, i am having serious trouble with the limit of integration part.
13. ### Area Inside Lemniscate Vector Calculus

oh yes, when i isolated for a i did remember the ^2 but i have no idea how to proceed from there
14. ### Iterated Integrals bounded by curves

Evaluate \int\int_{Q}\left(1 - x^{3}\right)y^{2} dA where Q is the region bounded by y=x^2 and x = y^2 So I have drew the graphs of y=x^2 and x=y^2 and found that they intersect at (0,0) and (1,1). Now I am confused what to replace Q with, but I think it should be this: please tell me if I am...
15. ### Area Inside Lemniscate Vector Calculus

Find the area inside the lemniscate ,which is described by the equation (x^2 + y^2) = 2a^2 (x^2 - y^2) I have no idea where to start so I found out what a lemniscate is.. but this didn't help me much. I have rearranged the equation for a: a = sqrt ( (x^2 + y^2)^2 / 2(x^2 - y^2) ) a = x^2...
16. ### Integration with squareroot

I have tried to do the hyperbolic trig way because I am stuck on mine and I can't seem to integrate the sec^3q this is what i have for hyperbolic, i am stuck and can't seem to integrate the last one integ (sqrt (1+x^2)dx) let x = sinh t dx/dt = cosh t integ (sqrt (1+sinh^2t) (cosh t dt))...
17. ### Integration with squareroot

I can't seem to figure out how to integrate this. integ ( sqrt (1+x^2) dx ) I am pretty sure I need to substitute the inside but I cannot figure out what. I have tried substituting x = tan theta, and i get stuck at integral (sec (theta)^3 dtheta) here is my work: (I am goin to use q as...