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

Expert Solution

I = SJ (2x-4) dA Solutioy : Let R: x² + y2 = 4 x=0,yan 2 ostyan x = 0 pey²4 (2,0) 310 I polar co-ordinatus put nar caso Yarsino then x² + y² = 82 - 8=2 and dA = dydx = r dodo Samo = o caso tano - I o = 1 thus vo T/2 . I. S (x 6030 - XSine) . x de do som k (916 - sho) (* do ce nter som le 940 - Suo)de 0 . Ja 64 1174 24 (2+0 - er 12- ] = -2.5882

milcah answered 2 years ago

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)

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

(1 point) The region in the first quadrant bounded by y=4x2 , 2x+y=6, and the y-axis...

(1 point) The region in the first quadrant bounded by y=4x2 , 2x+y=6, and the y-axis is rotated about the line x=−2. The volume of the resulting solid is: ____

Sketch the region in the first quadrant enclosed by y=2/x , y=3x, and y=1/3x. Decide whether...

Sketch the region in the first quadrant enclosed by y=2/x , y=3x, and y=1/3x. Decide whether to integrate with respect to x or y. Then find the area of the region. Area = Find the area of the region enclosed between y=4sin(x) and y=2cos(x) from x=0 to x=0.4π Hint: Notice that this region consists of two parts.

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.

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

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Use double integration to find the area in the first quadrant bounded by the curves y...

Use double integration to find the area in the first quadrant bounded by the curves y = sin x, y = cos x and the y-axis.

Use a double integral to find the area of the region. The region inside the cardioid...

Use a double integral to find the area of the region. The region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ). Can someone explain to me where to get the limits of integration for θ? I get how to get the pi/3 and -pi/3 but most examples of this problem show further that you have to do more for the limits of integration but I do not get where they come from?

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)

Multivariable Calculus [A] Consider the region R in the first quadrant that is outside the circle...

Multivariable Calculus [A] Consider the region R in the first quadrant that is outside the circle r = 1 and inside the four-leaved rose r = 2 sin 2θ). (A.1) Draw a sketch of the circle and the four-leaved rose (include the entire graph) and shade the region R. Feel free to use your graphing calculator. (A.2) Write the following double integral as an iterated integral in polar coordinates. Do not evaluate the integral in this part. Be sure to...

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