Double Integral : Horizontal and Vertical Simple Methods

I have managed to evaluate the double integral using the horizontal simple method, and answer 63. But when I reverse the order (vertical simple method) I cannot reach the same answer of 63, I get 65. 1) Evaluate the double integral of f(x,y)=x+4y^2 over the triangular region with vertices (-2,2) (4,2) & (1,-1) Check that r ...continues

Double Integral over a Square Region

Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x-y)sin(x+2y) over the square region with vertices at (0,0) (1,-2) (3,-1) & (2,1) (My notes from class-uses substitution, change of variables) I have let u=(2x-y) & v=(x+2y) using substitution (change of variables)

Verify Fubini’s Theorem for an integral evaluated over an equilateral triangle.

Verify Fubini’s Theorem for an integral evaluated over an equilateral triangle. (My notes from class-make a function up, similar to something used in question 1, but change powers of x & y.) You should discuss fully the reasons for the limits of integration in your solution.

Sketch the curve in polar coordinates given by r=2-4sin feta

4) Sketch the curve in polar coordinates given by r=2-4sin feta Find the area of the inner loop. Find the area of the inner loop for the general case: i.e. r=b-asin feta (0 isless than b is less than a)

Find the area bounded by one loop of a curve.

Find the area bounded by one loop of the curve given by x=sint, y=sin2t You should provide suitable notes to justify you solutions.

Find the maximum & minimum values

Find the maximum & minimum values over the square with vertices (0,0) (2,0) (0,2) (2,2) for the function f(x,y)=6x-x^2+2xy-y^4

Double Integral

Can anyone please show me how to solve these double integrals, with a step by step approach. I know the answer is 63 - but Ive tried so many times & I don't know where I'm going wrong. upper limits are 1&y=2 x+4y^2 dydx + lower limits are -2&y=-x upper limits are 4 & y=2 x+4y^2 dydx lower limits ar ...continues

Working between the integral

Can anyone show me the working between the integral in the enclosed file & the answer of A = 4/3

Verify Fubini's Theorem for an integral evaluated over an equilateral triangle

I am asked to verify Fubini's Theorem for an integral evaluated over an equilateral triangle. I am asked to fully discuss the reasons for the limits of integration in my solution. See attached file for full problem description.

Vector Problem : Force up Ramp

What would be the force required to push a 100-pound object along a ramp that is inclined 10 degrees with the horizontal?