What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval [0,20]? The average distance is (Type an integer, proper fraction, or mixed number.)

Q: Find the area of the region bounded by the parabola y = x 2  ,the tangent line to this parabola at…

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Q: The area bounded by the curve y 4x and the lines r = 6 ,x = 10 and a axis is

A: As per guildlines we can solve one question at a time. If you want answer of all please ask them…

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A:

Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its…

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: What is the area (in square units) bounded by the curve y' =x and the line x- 4=0?

A:

Q: What is the area of the largest rectangle that can be drawn with one side along the x-axis and the…

A: given curve is y=e-x2 find the largest area of a rectangle which has one side along the x-axis and…

Q: What is the area of the region bounded by the parabola y = x2 - x - 6 and the line y = -4. Round…

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Q: The area of the region bounded by the two curves y = x and y = 64 is Square Units

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Q: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: Find the area of the region bounded by the parabola y = 3x2, the tangent line to the parabola at (3,…

A:

Q: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

A:

Q: The area of region bounded by the parabola y? = 4x and the line %3D y = 2x – 4 is -

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: Find the area of the region bounded by the parabola y = 2x, the tangent line to this parabola at (4,…

A: Definition used -              Equation of a tangent line -                  (y-y1)=f'(x1)(x-x1)…

Q: Find the area of the region bounded by the hyperbola 9x2 - 4y2 = 36  and the line x = 3

A: Let the graph of the area of the region bounded by the hyperbola 9x2-4y2=36  and the line x = 3 is,

Q: The area of region bounded by the parabola y2 = 4x and the line %3D y = 2x – 4 is

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4 .

Q: Find the area of the region bounded by the hyperbola 25x² – 4y² = 100 and the line x = 3.

A: We have to find the area of the region bounded by the hyperbola 25x^2-4y^2=100 and x=3  Please see…

Q: The area of region bounded by the parab y = 2x – 4 is

A: Introduction: Integration is a method of bringing separate parts to form a whole. We find a function…

Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: What is the largest vertical distance between the graphs of the functions y = v and y = x in the…

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Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: What is the area of ​​the region between the parabola y=x^2-1 and the line y+2x=2?

A: The solution is given below in the next step:

Q: 4) Calculate the area of the domain bounded by the parabola y = x², the hyperbola y = and the line y…

A:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: The equation of the parabola is given by y = 4x2.Differentiate y = 4x2 with respect to x as follows.

Q: the

A: Given curve y^=x and y=√x  Line x-4=0   Find area ?

Q: Find the area of the region bounded by the parabola y = 2x2, the tangent line to the parabola at (3,…

A:

Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: Find the area of the surface formed by revolving g(x) = x^3 on the interval [0, 1] about the x-axis.…

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Q: Find the area of the region enclosed by the parabola y = 2 - x2 and the line y = -x.

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Q: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

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Q: 2) Find the area of the region bounded by two parabolas x = y2 - 5y, and x=3y - y? . Specify the…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

A: The shaded region is our required area

Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

A:

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

A:

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A: The given parabola is: y=2x2 The tangent line at (5,50) has the slope: mx=5=dydxx=5          =4xx=5…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by , the x-axis, and…

A:

Q: Find the area b0 und by Curves the y3= X-3

A: The region is bounded by y=9x2-36, y=0, x=1 and x=3

Q: The area of the region enclosed by the parabola y =2 -X and the line y = - xis equal to:

A: Given that that a parabolic equation and a line equation y = -x. And we find area enclosed by…

Q: Find the area of the region enclosed by parabola y=3-x2 and the line  Y=3-2x

A: We have to find the area of the region enclosed by parabola y=3-x2 and the line y=3-2x. The point of…

Q: The area bounded by the parabola x² = 2y, and the line x - y = -4 is 18 square units. %3D

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y , the…

A:

Q: What is the area of the region bounded by the parabola y = x^2 and the line y = x?

A:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A:

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A:

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 9 -x, and the line perpendicular…

A:

Q: The area of the region bounded by the two curves y = x² and y = 9 is Square Units

A: Draw the both curve than find their intersection points and integrate in that interval.

Q: An open rectangle box with volume 2m2 has a square base .express the surface s of the box as a…

A: Please find hand written solution.

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Q: Find the area of the region bounded by the curves, y = -6, y = 6 , the y – axis and the parabola y2…

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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.