Find the area of this region using the Fundamental Theorem of Calculus: 6x-3x dx 1

Q: The y of the area shown is ... R=l in 0.6in 1.6in

A: Area of the shown figure = area of semicircle - area of triangle   The area of a semicircle can be…

Q: Find the area bounded by y =-2x + 4,y 0, x 0 by using horizontal elements. -2 A. -2x + 4 dx y 2 - dy…

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Q: Evaluate the integral (2.x - y)dA, where D is the region in the first quadrant enclosed by the lines…

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Q: Evaluate the integral |r dA by making an appropriate change of variables where D is the rectangular…

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Q: Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: Find the area enclosed by the following curves: b). у %3DIn x3, у %3D In x, x %3D е

A: Given, y=ln x3 ,y =lnx, x=e

Q: Find the area of region enclosed by x = t - t", y =t – t, 0<t < 1 using Green's Theorem.

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Q: Find the area bounded by the given curves. 1. x^2=4y , 3x-4y+4=0

A: The area between the curves is the area between a curve fx and a curve gx on an interval a,b given…

Q: Find the area of region enclosed by x t - t*, y = t – t', 0 <t <1 using Green's Theorem.

A: solution is given below

Q: Find the Area bounded by the curves y? = x and x = 2y – y².

A: Draw the graphs of the given curves and mark the intersection area.

Q: Find the area enclosed by the xx-axis and the curve x=t^3+1x=t3+1, y= 2t-t^2y=2t−t2.

A: Given curves are x=t3+1, y=2t-t2.

Q: Find the area of the region that lies inside both cardioids. r = 1 + cos0 and r=1- coso

A: We have to evaluate the area of the region that lies inside both cardioids.…

Q: Use an iterated integral to represent the area of the rectangle shown in Figure

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Q: Find the area of region enclosed by x = t – t“, y =t – t°, 0 <t < 1 using Green's Theorem.

A: The solution are next step..

Q: Find the area of the region bounded by y = sin? x & y = sin³ x for 0 < x < T.

A: 1/6(3Pi-8)

Q: A Find the area bounded by y = e*, y = xe*² & x = 0.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: ind the moment with respect to x = 2a the area bounded by x = 2y and x2 4ay.

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Q: Find the area of the region R bounded by fx= sin x, gx= cos x, x=0 and x= 2pi.

A: We need to find the area between f(x) and g(x) where,

Q: ind the area bounded by the parabolas (x – 1)2 = 4ay and y² + 4a = 4ax. -

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Q: dx dy

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Q: Find the area obtain when the curve f(x) = x² – In æ, for 1 < x < 3, is rotated about the y-axis.

A: The surface area (S) of the curve y=f(x) rotated about the y-axis is given by: where a is the lower…

Q: Find a limit equal to the area shown. y = J 1 2 3 5

A: Here, fx=x, a=2 &amp; b=6. Now, ∆x=b-an=6-2n=4n

Q: Find the area enclosed by the given curves. y =- 4sin x, y = sin 2x, 0sxST O 8 O 1 O 16 O 4

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Q: Sketch the region R whose area is given by the iterated integral. dy dx

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Q: Find the area obtain when the curve f(x) = x² - In x, for 1 <x< 3, is rotated about the y-axis.

A: Given Data The equation is f(x)=x²-1/8lnx. The interval is 1≤x≤3.   The equation of the area of the…

Q: Find the area enclosed by the given curves. y = x3, y = 4x O 4 O 2 8 O 16

A: topic - area enclosed by curves

Q: 2y = x, x = 0, and y = %3D

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Q: Find the area bounded by y =e*, x=0, y = 0, and x= 2.

A: topic - area bounded by curves

Q: Find a limit equal to the area shown. y-sin (21)

A: Given y=sin2x To find the width π2-0n=π2n So now ∑i=1nf0+π2niπ2n Which is,…

Q: Find the area between y= e" and y = e over [0, 1]. %3D A =

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Q: Sketch the region R whose area is given by the double integral. 9. 3 6. dy dx

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Q: Evaluate the integral N2 (x2 – 2y?) dA, where R is the first quadrant - region between the circles…

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Q: Find the area of the shaded region 14 LA bounded above by y = 2, bounded b TE lo 1)

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Q: Evaluate the integral R(x² – 2y²) dA, where R is the first quadrant region between the circles of…

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Q: ind the area of the region using integration.

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Q: Let D be the region on the right half plane which lies below y=x+1 and inside the ellipse = 1. Which…

A: Given the equation of a straight line y = x + 1 and the equation of ellipse x2+y24=1. We need to…

Q: Find the area of region enclosed by x = t – t", y =t – t°, 0 < t < 1 using Green's Theorem.

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Q: Sketch the region enclosed by the curves x = sin 3y and x = y, and compute its area as an integral.…

A: We have to find the area between the curves.

Q: Determine by direct integration the second moment of area about the x-axis [units^4] of the area…

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Q: Find the area of this region using the Fundamental Theorem of Calculus: 2+cos x dx

A: Consider  ∫0π2+cosxdx

Q: Given the area of the region enclosed by y = 2 – x´ and y =-x, identify the integral that represents…

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Q: Find the area obtain when the curve f(x) = x² - In r, for 1 <a< 3, is rotated about the y-axis.

A: The area obtained when the f(x) is rotated about the y-axis is given as: where a is the lower limit…

Q: Find the area of the region R bounded by y2=a2−ax, y=a+x.

A: Consider the given curves Let sides of the equations are the same. Equate right sides, The limit…

Q: A Find the area bounded by y = e*, y = xe* &x = 0.

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Q: Find the area in square units bounded 1) y2 = 4x, x=0 to x= 4

A: Area Bounded by the curves :   If x=f(y) and x= g(y) be two continuous function on a,b and f(y)…

Q: Find the area of the region bound by the x-axis, f(x) = sin x, x = -. 3' TT and x = 2

A: The equation of the curves are : C1 : fx = sinx C2 : y = 0 C3 : x =-π3 C3 : x =π2 To evaluate : The…

Q: Find the area of the region bounded by y=x2, y=1, and x=0 revolved around x=2 using both the shell…

A: Shell method: Let a cylindrical shell which is at distance x from the y-axis, having thickness dx,…

Q: Sketch the region enclosed by 2y=4 sqrt(x), y=3, and 2y+3x=7. Decide whether to integrate with…

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Q: find the area of the cylinder z=x+y2 that lies below the second-quadrant area bounded by x axis,…

A: Given that: find the area of the cylinder z=x+y2 that lies below the second-quadrant area bounded by…