using / for integral Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the...

using / for integral

Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the trapezoidal region with vertices (1,0), (2,0), (0,2), and (0,1)

Expert Solution

Colby Messinger answered 2 years ago

Calculate the double integral ∫∫Rxcos(x+y)dA∫∫Rxcos⁡(x+y)dA where RR is the region: 0≤x≤π3,0≤y≤π2

1) Evaluate the double integral ∬Dx^2 y dA, where D is the top half of the...

1) Evaluate the double integral ∬Dx^2 y dA, where D is the top half of the disc with center the origin and radius 2 by changing to polar coordinates. 2) Use a double integral to find the area of one loop of the rose r= 6cos (3θ). 3) Use polar coordinates to find the volume of the solid below the paraboloid z=50−2x^2−2y^2 and above the xy-plane.

Find the double integral of region (2x-y)dA, where region R is in the first quadrant enclosed...

Find the double integral of region (2x-y)dA, where region R is in the first quadrant enclosed by the circle x2+y2=4 and the lines x=0 and y=x

Use the given transformation to evaluate the integral. (12x + 8y) dA R , where R...

Use the given transformation to evaluate the integral. (12x + 8y) dA R , where R is the parallelogram with vertices (−1, 3), (1, −3), (2, −2), and (0, 4) ; x = 1/ 4 (u + v), y = 1/ 4 (v − 3u)

1. Evaluate the double integral for the function f(x,y) and the given region R. R is...

1. Evaluate the double integral for the function f(x,y) and the given region R. R is the rectangle defined by -2 x 3 and 1 y e4 2. Evaluate the double integral f(x, y) dA R for the function f(x, y) and the region R. f(x, y) = y x3 + 9 ; R is bounded by the lines x = 1, y = 0, and y = x. 3. Find the average value of the function f(x,y) over the plane region R....

evaluate the integral by making an appropriate change of variables double integral of 5sin(25x^2+64y^2) dA, where...

evaluate the integral by making an appropriate change of variables double integral of 5sin(25x^2+64y^2) dA, where R is the region in the first quadrant bounded by the ellipse 25x^2 +64y^2=1

1)(a) Approximate the value of the double integral, ∫ ∫ R x 2 ydA, where R...

1)(a) Approximate the value of the double integral, ∫ ∫ R x 2 ydA, where R = [−1, 5] × [0, 4], using the midpoint rule with m = 3 and n = 2. (b) Evaluate the double integral in the part (a), evaluating the corresponding iterated integral. 2)Let D be a region in the xy plane, between the graphs of y = 2 cos(x) and y = − sin(x), for 0 ≤ x ≤ π 2 . Sketch D...

Evaluate the integral by making an appropriate change of variables. 3 cos 5 y − x...

Evaluate the integral by making an appropriate change of variables. 3 cos 5 y − x y + x dA R where R is the trapezoidal region with vertices (6, 0), (10, 0), (0, 10), and (0, 6)

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) =...

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) = ? Please complete this table. I am having trouble converting functions from polar to cartesian in the three dimensional plane. I understand that x=rcos(?) and y=rsin(?) and r2 = x2 + y2 , but I am having trouble understanding how to apply these functions.

Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=sin(x)i+cos(y)j+4xzkF(x,y,z)=sin(x)i+cos(y)j+4xzk and C is given by the vector function r(t)=t3i−t2j+tkr(t)=t3i−t2j+tk...

Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=sin(x)i+cos(y)j+4xzkF(x,y,z)=sin(x)i+cos(y)j+4xzk and C is given by the vector function r(t)=t3i−t2j+tkr(t)=t3i−t2j+tk , 0≤t≤10≤t≤1.

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