- a) Evaluate (3 – 6xy)dA where D is the region shown below.

Q: Find the area of the ring between two circles (shaded in purple).

A: Given,           The figure is shown below :

Q: sin x – e-* = 0, [0,1]

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is…

Q: Use the change of variables X = u, y = uv to evaluate ex dA, where R is the region R in the xy-plane…

A: Solution: The objective is to find the value of ∬ReyxdA where R is the region in the xy-plane…

Q: Evaluate R y sin (y² x) dA using the substitutions

A: Clearly, one may find that in the original region Now one may put It will change .And one may also…

Q: change the Cartesian integral into an equivalent polar integral.

A:

Q: 3. Evaluate the given integral Q using polar coordinates. Q = dA; R is the region bounded by r2+ y?…

A:

Q: R 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9 ≤ x² + y² ≤ 25 by…

A: The objective of this question is to evaluate the double integral of the function (x² + y²) over a…

Q: Find the area of the region common to the interior of the of the cardioids r = and r = 1 + cose…

A:

Q: Use the given transformation to evaluate the integral. [[ 9 cos(3 (v + X)) d dA where R is the…

A:

Q: Evaluate the given integral SS₂ e-x² - y² JA where Coordinates Semicircle polar bounded by the by…

A:

Q: Find the area contained in the cardioid defined by x² + x²+ +y? (Hint: First convert to a polar…

A:

Q: Find the ÿ Coordinate of the centroid of the shaded area shown in Fig. below. 2" 2 2y³ = x² 2

A: We have to find the y  co-ordinate of the centroid of the figure

Q: Consider the double integral cos(a² + y²)dA where R is the region above the r--axis in R between the…

A: Iterated integral and polar coordinates

Q: Evaluate the integral [(6-2²) dz where C is the anticlockwise square contour with vertices at 1 + i,…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Use the given transformation to evaluate the integral. S SR y?dA, where R is the region bounded by…

A: Solution:

Q: 10 a . b. d(f,g)

A:

Q: Use the given transformation to evaluate the integral. 6 sin(81x2 + 25y2) da, where R is the region…

A:

Q: (a) Evaluate I = SSSp cos(r2 + y?) dA, where E is the region that lies inside the cylinder x2 +y² =…

A: (a). Consider the triple integral To evaluate the integral, use the cylindrical coordinates. So,…

Q: The double integral f 2xy dA over the rectangular region R = {(x,y) E R, 0<x<4 and– 1<y<0}is equal…

A:

Q: Evaluate the given integral by changing to polar coordinates. x² - y² dA, where D is the region…

A:

Q: Evaluate the double integral Sr S f(r,0) dA, and sketch the region R. 9– r² dr d0

A:

Q: Evaluate the integral in terms of Beta function: , (1- a)'dr (SAN) OP(4, 2) OP(1, 4) OP(8,4) OP3,4)

A:

Q: h y=hx b- a y = (h)(x-b)

A:

Q: 3. Let R be the region shown. a) Set up an integral in polar coordinates to evaluate ff xydA R -3…

A:

Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

A:

Q: Find ff xy + y dA, if D is the region: x² + y² ≤ 1, (x - 1)² + y² ≤ 1 using polar coordinates.

A:

Q: Evaluate the following double integral a) Evaluate 8xy dxdy=? 1 b) Evaluate the following integral…

A: A)∫12∫038xy dx dy=∫12 8yx2203 dy=∫1236y dy=18y212=18(4-1)=54

Q: Set-up the integral which yields the ar

A:

Q: Calculate the double integral f SR T cos(2a + y) dA where R is the region: 0 <I<0 <y

A: To find- Calculate the double integral ∬Rx cos2x + y dA where R is the region: 0 ≤ x ≤ π6, 0 ≤ y ≤…

Q: 1 x² dA, where R is the region enclosed by the circles x² + y² = 1 and x² + y² = e² + y² , by…

A:

Q: Evaluate J sin(x + y)dxdy, R where R is the area bounded by the lines y = x, x+y= π/2 and y = = 0.

A: We can find the integral.