R zone; Being the first region of the coordinate plane bounded by the lines y=0, y=√3 and the circle x²+y²=9, Calculate the integral given in the picture.

Q: Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double…

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Q: Find the area of the surface x2 - 2 ln x + sqrt(15)y - z = 0 above the square R: 1<=x <= 2,…

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Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

Q: Find the area of the surface generated by revolving the semicircle y = √1 − x about the x-axis over…

A: Given that, y=1-x. dydx=121-x-12·-1=-121-x 1+dydx2=1+-121-x2=1+141-x=1+14-4x=4-4x+14-4x=5-4x4-4x

Q: Find the surface area of revolution about the x-axis of y = 3x + 4 over the interval 1 < x < 2

A: Answer

Q: Evaluate the double integral x+y dA R y - 4 , y = 4–7x and the x-axis. 7 over the region R where R…

A: Let's find.

Q: The area of the finite region enclosed by the curves y = 3x and y 27 - a is given by the definite…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.

A: First we need to find the x coordinates of the points at which the graphs of the functions…

Q: The region enclosed between the curves y=x² – 3x + 5 and y = x +2 can be computed by the integral…

A: area between two curve can be calculated as following:-

Q: Find the area of the plane region bounded by the curves y = Vx - 1, y = 3, the x-axis, and the…

A: Region bounded be the curves is given, we need to find the area of the region. Firstly,  we'll draw…

Q: b) Use double integral to find the area of the region that is bounded by the lines y = x - 2 and y =…

A: Double integral is used to integrate the function of two variable over two-dimensional region.…

Q: Find the region bounded by the curves y = x and y = x² using a dx integral.

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Q: Shade the area of the region bounded by the parabola, x² +p² – 2(p + 7)x – 5y + 59 + 14p = 0 and the…

A: We rewrite the equations  of parabolas and straight lines with p=9 as…

Q: Find the surface area of revolution about the y-axis of y=6x+3 over the interval 0 ≤ x ≤ 3

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Q: Q2 : Sketch the region of integral and determine the v the function z = 2x-y2 over a region bounded…

A: Introduction: The volume of a function f(x,y) with the region a≤x≤b, c≤y≤d is given by,…

Q: (24) x+1 = y°, x= y,y = 0, y = 1

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Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 0≤x≤1

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Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

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Q: Sketch the region enclosed by the curves and find its area. 1 ¤ = 0, y = 1, y= e³ x = - NOTE: Enter…

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

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Q: Evaluate the integral I dA where Dis the region bounded by the curves r+y 0 and r +y==-12

A: From the given integral: I=∫∫DxdA From the given curve the bounded region is as shown below: Now…

Q: The area bounded by the curve y = VT, the y-axis and the line y = 2 is revolved about the line y =…

A: The given curves arey=x, and the y axis and the line y=2 is revolved about the line y=2now since…

Q: Set-up the integral using horizontal element for the area of the plane region, 0≤x≤ = 21. bounded by…

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Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: Find the area bounded by y? = 4a (y – x), y² = 2a (x + 2y – 3a) and x-axis. Show complete %3D…

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Q: Find the area of the region bounded by the given curves. a. y = 2 – x2, y = x² b. у%3D Зх + 2, у %3D…

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Q: Q1) Find plane area bounded by y = 2, y = x, and y = 0.5x using double %3D Integration .

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Q: Find the value of the line integral foF dr without using Green's Theorem, where F(x, y) = (x + y)i +…

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Q: y² – 2, Use an iterated integral to find the area of the region bounded by the graphs of x = y-x= 4,…

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Q: Express the area of the region bounded by the given lines and curves as an iterated double integral.…

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Q: Find the surface area of revolution about the x-axis of y=4x+1 over the interval 1≤x≤2

A: y=4x+1, 1≤x≤2 Differentiating with respect to x, we get dydx=41+0=4

Q: The area of the region bounded by the curves y = 2+|x-1|, and y = %3D 2+3 is given by the integral…

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Q: * Let R be the region in the first quadrant bounded by x^2 +y^2 = 4, y^2 = -x+4 and y=0. Set up the…

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Q: Shade the area of the region bounded by the parabola, x2 +p 2– 2(p + 7) x - 5y + 59 + 14p = 0 and…

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Q: Sketch the region enclosed by the curves y=2 and y =-2x+3 then find its area using the appropriate…

A: Consider the following curves: y=-2x+3y=2 Intersection point of curves: -2x+3=2-2x=-1x=12…

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = =9y-y2 and y = 2

A: Follow the steps.

Q: 343 2 1. y = x² - 9 and y = x + 3 (Answer: 6 s. u.)

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Q: Q2) Find plane area bounded by functions y = x,y 3,and x = 5.

A: We have to find the area bounded by the functions: y=x, y=3, and x=5For y = 3 we have x = 3

Q: Sketch the region whose area is given by the definite integral. (3x + 3) dx y y 20- 20 15 15 10 10…

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Q: Find the integral that represents the surface area obtained by rotating around the x-axis the graph…

A: To find the integral representation for the surface area under the given conditions.

Q: The area of the region enclosed by curves is    curves x=2y^2              x=0 , y=3

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Q: Express the area of the region bounded by the given line and parabola as an iterated double…

A: The equation of the line and the parabola are: C1: y = x2…

Q: (b) Use Green's Theorem to evaluate ſ. 3ysin(x)dx + 5xdy where C is the boundary of the region…

A: Solution:Given∫c3y sinx dx+5xdyFormula:∫cPdx+Qdy=∬ ∂Q∂x-∂P∂y dA

Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: Iculate the integral (2² - y2) dA nain D is bounded by y = r and y = 4x for I > 0. ving of the…

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Q: Find the surface area of revolution about the y-axis of y = 5x + 1 over the interval 0 < x < 3

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations y = 4…

A: Given: The region bounded by the graphs of the equations y=4-x2, y=x+2.

Q: Set-up the integral for the area of the plane region bounded by 4 °^(-x (-x²+3x+4)dx -1 8 (5+…

A: A detailed solution is given below.

Q: Q2) Find plane area bounded by functions y = x,y = 3,and x = 5.

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