What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0, 20]?

Q: ind the point P on the line y = 5x that is closest to the point (78,0). What is the least distance…

A: This question is related to straight line. we will solve it using the condition of shortest distance…

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

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

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Q: Find the exact length of the curve. y = In(sec(x)), Osxs n/4

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Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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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 largest vertical distance between the graphs of the functions y = Va and y x2 in the…

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Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: y = 3x – 1 + Ce-3x | x = Cey?

A:

Q: Find the area of the segment of a sphere formed by revolving the graph of y = √25-x2,0 sxs 4, about…

A: Given y=25-x2, 0≤x≤4 A sphere is a geometrical object that is a three-dimensional analogue to a…

Q: Find &y:3mは や Rirst * = In in the the between the Curve area the line メ=H quadraut

A: We first sketch the region using a graphing calculator

Q: Find the length of the curve y=lnx from x=1.5 to x=3.

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Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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Q: Find the length of the curve y = x2 from x = 0 to x = 7.

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Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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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 are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

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

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Q: Find the arclength of y = 3x3/2 on 2 < x < 4

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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 slope of the tangent line to the parabola y= 2 +x−x^2 at the point (0,2).

A: Simply take the derivative of the given equation and substitute the given point.

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Find the orthogonal trajectories of the family of parabolas through origin and foci on axis.

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Q: + 2 Find the length of the curve y = from the point where a = 1 to the point where x = 2.

A: The length s of a curve with the function y=f(x) for the interval of x from a to b is given by the…

Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = V 25 - x2, 0 sx< 4,…

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Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: Find the arclength of y 3x3/2 on 1 < x < 3

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Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: Find the length of the curve y Inx at (2<x< 4)?

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Q: Find the length of the curve. y= x? + from x = 1 to x = 5

A: Please refer the attached image for complete solution. THANK YOU.

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 arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: I need to solve this question

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Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

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 tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: Find the length of the curve. 33) y-승. from x = 1 to x= 5 2x

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

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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: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.