Evaluate the following integrals by converting to polar coordinates: 2 (a) / VI=z² (1+x² + y2)2 dydx (b) L V+y° dxdy V2-x² (c) L (x + y) dydx

Q: Transform y = V3'x into polar form.

A:

Q: Given the polar function r = {a(1-e^2)} / {1+ecos(theta)} find an expression for dy/dx, simplified…

A: Given that r=a1−e21+ecosθ To find an expression for dy/dx.

Q: Q1) Evaluate the integral dy dx using polar coordinate

A:

Q: 1/2 VI (Iy xy <p p xp

A:

Q: Convert to polar coordinates with r > 0 and 0 < 0 < 2T. (- 1, 1/3)

A:

Q: Find e-a* -y" dx dy using polar coordinates.

A:

Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: cosh (0.375-j0.485) express in polar form

A:

Q: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

A: Using Cartesian coordinates to polar coordinates.

Q: Transform (0, y) from rectangular into polar form (here y is any negative number).

A: We have convert rectangular coordinates (0 , y) into polar coordinates: Where y is negative number-

Q: Evaluate f" Na-*) /x² + y² dydx, using polar coordinate. -a

A:

Q: 9-y² 2. Evaluate the integral (2.x + y) dady by converting to polar 9-y? Coor- dinates.

A:

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Evaluat lna %3D

A: the question is taken from calculus  and in which we have to  find the integral value of I now we…

Q: 1 @[₁ 1. Use polar coordinates to evaluate -1 JO /1-x² (x² + y²)³/2 dy dx.

A: By using polar coordinates to evaluate the following integral.