13. Let a region be enclosed by y = x² and y = V and its area is given by (Vx– x²) dx. What are the values of a and b? a. a = -1,b =1 b. a = -1,b = 0 c. a = 0, b = 1 d. a = -1,b = 2 e. None of the above

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A: To find the area under y=2x from x=0 to x=1

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Q: • 16. The area which is inside r r = 3-sino 5sin 0 and outside the limacon

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A:

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A: Solution

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A:

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Q: 13. The volume of a sphere with radius r 2 is given by * 8-2r dr a. b. f,2-x°dx none of the above

A:

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A:

Q: 7. Find the area bounded by the curve y = x? +x + 4, the x-axis and the ordinates x = 1 and x = 3.

A: Given; y=x^2+x+4

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A: Given: curves y=x^2+10x , y=2x+9 We have to find the area between the curves

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A:

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A:

Q: 4) The area between y= In x and y = 2ln x up to x= e is:- A) = 7 B) = 1

A:

Q: 5. Evaluate z dV where E is the region bounded below by x2 + y? + z2 = 4 and above %3D E by x? + y?…

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Q: 4. Find the area of the region bounded by y = sin x and y = sin? x between a = 0 and a =

A: The region bounded by y=sinx and y=sin2x between x=0 and x=π2 Note:    Multiple questions are given,…

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A: we have been given the function y=3x2-12 and y=0 and the formula of the area under the curve is…

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A:

Q: 10- Evaluate JS where E is the region that lies inside the cylinder x² + y²dV E x? + y? = 16 and…

A:

Q: 9. Find the area of the region between y = sin 0 and y = sin e , between 0 = 0 ande = n/2. %3D

A: To find the area of the region between,  y = sin3 θ  and y = sin θ Between θ = 0 and θ = π/2 The…

Q: 12. What is the area of the region enclosed by y = x² and y = x? b. d. e. None of the above -IN -IM…

A:

Q: 3. Find the area of the region enclosed by the given curves. y = Vx + 2, 1 y = x = 0, x = 2 %3| x…

A: Recall: If f(x) and g(x) are two continuous function and f(x) ≥g(x) on the closed interval [a,b] ,…

Q: the region described. 5 1 ded by y = 7 and y = 4 2 1-X egion is approximately

A:

Q: 4) The area between y = In x and y = 2ln x up to x= e is:- = 7 A) B) = 1

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: 1)Find the area bounded by the given curves: a)y = 6x2 and y = 24   b)y = 3x2 − 12 and y = 0

A: The given function are y=6x2 and y=24. The area bounded by the given curves as shown below:

Q: Let A be the area of a circle with radius r. If dr/dt=5, find dA/dt when  r=2.

A:

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A: Consider the given: y=cosx,y=cosx−c and x=0cosx−cosx−c=0−2sin2x−c2sinc2=02x−c2=0x=c2 Find the area:…

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A:

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A: Given that,

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A:

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A: The area under the given curve = 48.4

Q: 4 / Find the area of the region enclosed between the curves y%3= cos 2x, y=0, x-TT/4, x- TT/2 ? ans/…

A: we allowed providing one solution at a time. Please upload the rest questions seprately.   Question…

Q: 18. Find the area of the region enclosed by the curve y = (1- x)²; 0<x< 1. (in QI)

A:

Q: 1. Find the AREA of the region bounded by y = y=x, and y = 5. Express the answer as an exact value…

A: Please see the explanation below

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: Since you have posted multiple questions i can do first question as per our company guidelines…