Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve y = 4 – x².

Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: 11. Find the area bounded by the curve 5y²-16x and the curve y²=8x-24. A. 30 sq.units C. 16 sq.units…

A: We need to find area bounded by curve.

Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

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Q: Find the area bounded by the curves: y=-3x/(x2+2) , x2+y2=5, and x=0. This area is in the fourth…

A: The solution are next step

Q: (b) Find the area enclosed by the curve y = 4x2 and the x-axis between x = -2 and x = 2. %3D

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Q: Find the length of the curve y 2ln(x) from x 1 to x =4. %3D

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Q: What is the total area of the curve y T and the x-axis between I =1 and x = -1? %3D -1

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Q: Q4: Find the area enclosed by the curves: y = x² and y = -x² + 4x.

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Q: 2. Find the area enclosed by the curve y2 = x6 (1- x²)³.

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Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal distance…

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Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y = 12…

A: This question is based on application of Integration.

Q: find the length of the remaining part of the y = x³/12 + 1/x curve between the x = l and x = 2 apfog…

A: We have to find the length of the remaining part of the curve y=x312+1x between x=1 and x=2

Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: Q2. Find the area enclosed by the curve y = x³ – 3x² + 2x and the x-axis.

A: To find the area enclosed byy=x3-3x2+2x and x-axis

Q: For a χ2-curve with 19 degrees of freedom, find the χ2-value that has area a. 0.025 to its right. b.…

A: a) Degrees of freedom is 19 The chi-square value that has area 0.025 to its right is given below:…

Q: Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not…

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Q: Find the areas enclosed by the following curves: (e) x + y2 = 3 and 4x + y² = 0

A: Solve using application of integrals

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

A:

Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

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Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

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Q: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: FIND THE LENGTH OF THE CURVE 9y = x(x – 3)´ from X = 1 to x = 4 %3D 10

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Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

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Q: Rotate the graph of g(x)=e^(−6x) on the interval [0,8] about the x-axis to generate a surface with…

A: Given that g(x)=e-6x To find the surface area by rotating the graph of g(x) on the interval [0,8]:

Q: 4. Find the area between the curves y = x2(x – 3) and y2 + 8y – 16x + 48 = 0

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Q: Find the area of the surface gener- ated when the given curve is revolved about the given axis. y =…

A: Given: y=4x+6,  0,5

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = /5x +…

A: To find the surface area generated when y=√(5x+3) is revolved around the x-axis on [0,5]

Q: B) Find the area between the parabolas x = y² - 1 and x = 2y² - 2

A: Topic = Area

Q: Find the area of the region lying between the x-axis and the curve y = In(7x) – 1 to the right of…

A: Consider the function y=ln7x-1x2. Find region between the curve to the right of line x=e and  x-axis…

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: Find the area bounded by the curve y=- 16 A 10 square units B) 16 square units Ⓒ 8 square units (D)…

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Q: ind the exact length of the curve. X = 8 4y2' 1sys 2

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Q: Find the length of the curve of y=x³/2 from x=1 to x=4.

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Q: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: Find the y²=x,x²-2x +3y=2 area between the two curves..

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Q: The positive number c for which the curve yd- divides the area under the curve y 2209- from O to 47…

A: Given

Q: What is the longest distance from the curve x ^ 2 + xy + y ^ 2 = 16 to the origin?

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Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Find the area of the “triangular” region in the first quadrant that isbounded above by the curve y =…

Q: (#2) Find the area of the surface generated by revolving the curve about x-axis for f(x) = 2Vx on…

A:

Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

Q: What is the length of the -3< x S3 segment of the y = v36 – x2 www vwwb w e curve?

A:

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: Y=Ğ jfor exS3; about The X-axi's

A: The formula for the surface area generated by rotating the curve  A=2π∫abf(x)a+(f'(x))2dxHere…

Q: Find the area between the curve y = x(x 3) and the ordinates x = 0 and x = 5. LA B

A: Topic = Area

Q: Find the area enclosed between the X-axis and the curve y = (x +1)°,0 < a < 3.

A: The area under a curve is the area between a curve fx and the x-axis on an interval a, b given…

Q: Find the area between the curve y = x = 0 and x = 5. x(x 3) and the ordinates - LA B 3

A: