A- Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx.dx, and compare the estimate with exact result. B-Convert the point (-6, -3) from rectangular to polar coordinate.

Q: tegral by transforming to polar coordinates.

A:

Q: Find the area enclosed by the given parametric curve and the x-axis.

A: Given : Given parametric curve are x=t3+1 , y=2t-t2 We want to find the area enclosed by the given…

Q: Convert the integral to polar coordinates.

A: Polar coordinates Option B

Q: 4. Evaluate √² +² dzdy by changing to polar coordinates. Sketch the region of integration..

A:

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

A:

Q: Given the following table: X f(x) Calculate f(1,3) by Lagrange Order 3! 0,0 1,0 0,5 2,119 1,0 2,910…

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: Use the change in variables s = x + 4y, t = y to find the area of the ellipse x^2 + 8xy + 17y^2,…

A: We have to find the area of the ellipse  x2+8xy+17y2≤1. Use the change in variables s=x+4y and t=y…

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

A: Using Cartesian coordinates to polar coordinates.

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: +³ 3 y=a+t, √a ≤ t ≤ √a X || +at,

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: Graph the polar equations r = 3-2sin(theta) and r = 2 . Find and label any key points needed to find…

A: Given that, Polar equations, First, we need to find points of intersection of two graphs: By…

Q: Find the area inside the cardioid with a polar curve of r=4+4cos(θ).

A: Find the area of inside the cardioid with a polar curve: