7. By using the double integral in polar coordinate, find [S for the region 1+x²+y² in the first quadrant bounded by x² +y² = 4,y = 0,y = x.

Q: 9) Use Fubini's Theorem to compute the double integral ƒƒ_ƒ(x,y)dª_where…

A:

Q: 1. Evaluate the double integral fSp xedA where R is the region bounded by y = 4 – x and y = 0 and x…

A:

Q: Calculate the double integral √ √(8x + 2y + 16) dA where R is the region: 0 ≤ x ≤ 1,0 ≤ y ≤ 4.

A: The objective is to evaluate the double integral.

Q: 5) Use an iterated integral to find the area if the region. y y = 4– x2 3 2+ 1 3 4

A:

Q: Use Green’s Theorem to evaluate the line integral  (x^2 − 2xy) dx + (x^2 y + 3) dy where C is the…

A: The given problem is to evaluate the given integral in the contour using the green's theorem in the…

Q: The double integral 2xy³dA over the rectangular region R {(x, y) E R“, 0 < xS 4 and – 1 S y< 0} is…

A: The double integral ∬Rfx, ydA can be written as ∬Rfx, ydxdy. We have given the rectangular region as…

Q: 1 -drdydz JSJ (x² + y² + 22)#

A: Use spherical coordinate system to solve it.

Q: 3. Sketch the region and evaluate the iteraterd integral (a²y – ry?)dydx. 2.0 1.5+ 1.0 0.5 0.0 0.0…

A:

Q: 2) Calculate the integral the regions descri bed. over / 2x- 5xy- 3y² dA. On a y = (x-1) /3 , y= -2x…

A: Bounding lines y=x3         → 3y-x=0y=(x-1)3→3y-x =-1y=-2x    →y+2x=0y=1-2x  →y+2x=1

Q: Calculate the double integral / /R x cos(x+ y) dA where R is the region: 0 < x <,0 < y< 4

A: Explanation of the answer is as follows

Q: Sketch the region R whose area is given by the iterated integral. 16 – y2 dx dy 3 2- 2 6 8. 10 12 14…

A: option B

Q: 19) Evaluate the double integral for f(x, y) = 2y+x over the rectangle region R defined by 3 ≤ x ≤ 4…

A:

Q: evaluate the double integral xy cos y dA over the given region R = [-1,1] × [0, 7 ]

A:

Q: Compute the double integral S, 2xy dA, where R is the region bounded by x = y² and y = x.

A: We are given that the region R is bounded by the curves x=y2 and y=x. So first, we need to find the…

Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.

Q: Question 8. Use a change of variable to compute the integral 10 R x+ y where R is the triangular…

A: To evaluate the integral by changing the variables x,y into the new variables u,v, use the following…

Q: 4. Compute the integral x sin (xy) dA where R is the region 0 <x <1 and 0<y < .

A:

Q: 2. Evaluate the double integral STR (x+ y) dA over the region R give by R= {(x, y) : y > x², y <…

A:

Q: 5. Show that, in the region bounded by y = Vx and y = x2 the following double integral 3 (х + у) dA…

A:

Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

A: off

Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. = x²…

A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…

Q: 2 In y 1) Sketch the region R and express |e* dxdy as an equivalent double integral with the order…

A:

Q: 3. Use a suitable change of coordinates to calculate the integral / x² – y² dA, where R is the R…

A: The region R is given by

Q: 4. the value of the given integrals | z - i | = 2,(z € C) around the circle compute for positive…

A:

Q: Verify Green's Theorem by evaluating both integrals for the given path. [x² αx + x² or = // (+1) ++)…

A:

Q: Determine the integral of x y dx dy. Use inner limits=0 to (y + 1) and outer limits=0 to 1.

A:

Q: 3. Set up an integral for the double integral and use the more convenient or integral over the…

A: Given integral is, ∬R2yx4+1dA R is the region bounded by y=2x3/2, y=0, x=1,x=2

Q: 1. dydx yt + 1 0.

A: Explanation of the answer is as follows

Q: 4. Sketch the region of integration and evaluate the double integral by changing to polar…

A:

Q: \ Calculate the double integral Rx cos(2x + y) dA where R is the region: 0< x < ,0 < y

A: According to question, Let I =∫∫R x cos 2x+ydA,0 ≤ x ≤ π6,0 ≤ y ≤ π4

Q: Calculate the double integral fp x cos(x + y) dA where R is the region: 0 < x < ,0 < y <

A:

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

A:

Q: Evaluate the double integral Jl, x dx dy where the region R is bounded by: 3 y = 4x – 3, y =x +, y =…

A:

Q: Calculate the double integral S TR (2x + 8y + 16) dA where R is the region: 0 < x < 4,0 < y < 1.

A: we have to find the double integral  ∫∫R(2x+8y+16)dAwhere R is  the region 0≤x≤4,0≤y≤1

Q: Set up the definite integral that gives the area of the region. Yı = (x – 7)3 Y2 = x – 7 dx J6 y 1.5…

A: Given problem:- Set up the definite integral that gives the area of the region. Y1 = (x-7)³ Y2 = x -…

Q: Find the limits of integration for double integral [[ f(x,y)dxdy over the given D region of…

A: Introduction: When a double integral is described within a region enclosed by a circle, we can…

Q: 4. Evaluate the integral (a + y) dA; where D is the region bounded by y = and the line y = }- x.

A:

Q: The centroid of the region bounded by sin x < y< cosx, and 0<x<7/4 is, TV2-4 b) 1 1 a) 4(42 +1) 4(v2…

A:

Q: Calculate the double integral / Rx cos(2x + y) dA where Rl is the region: 0 <x<,0 < y< 6. 2

A: Here we have to find the value of double integral.

Q: at is the ans

A: Introduction: Integration is a method of bringing separate parts to form a whole. We find a function…

Q: Calculate the double integral S SR r cos(x + y) dA where R is the region: 0 < ¤ <,0<y 0.064

A:

Q: Find the integral of xy over the region bounded by the x axis, the line y=x and the line x=1 using…

A: Here we have to find the integral of xy over the region bounded by the x-axis , the line y=x and the…

Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x2, x = 7 %3D

A:

Q: area of the region. y1 = x2 + 2x + 2 y2 = 2x + 11

A:

Q: 4. Compute the value of the double integral fSRe-xydxdy, where R is the region bounded by the lines…

A:

Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

A:

Q: Calculate the double integral ∫∫R xcos(2x+y)dA where R is the region: 0≤x≤π/6, 0≤y≤π/2

A: the double integral ∫∫Rxcos(2x+y)dA where R is the region: 0≤x≤π/6, 0≤y≤π/2

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.