What is the average distance between the parabola y = 10x(22 - x) and the x-axis on the interval [0,22]? The average distance is . (Type an integer, proper fraction, or mixed number.)

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: Determine the area of the largest possible rectangle whose base is on the x-axis and the top two…

A: The given curve is y=9-x2

Q: Find the approximate area between the curve Ax) = -2x + 32x + 5 and the x-axis on the interval [0,…

A: The given data is:   To find the approximate area.

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 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: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

Q: Estimate the area between the curve y = x^2 - 2x + 5 and the x-axis between x = 0 and x = 3 using 6…

A: Given, y=x2-2x+5 Here, a=0, b=3 and n=6 Therefore, ∆x=b-an3-06=12=0.5 Therefore the intervals are,…

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: The area of the region enclosed by the parabola y = 2 - x? and the line y = -x is :

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 = 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 total area of the shaded region (area constrained by curves) y = -2r4 -2

A: The area of the shaded region is given by  ∫abf(x)-g(x)dx Where a and b are limits of x f(x) and…

Q: Find the area of the region bounded by the parabola y = x², the tangent line to this parabola at (1,…

A: Given data: The equation of the parabola is y=x2. The given point is (a, b)=(1, 1). The slope of the…

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

A:

Q: What is the volume of the solid stretching over the x-interval |0, 2| whose cross-sections are…

A: Given,  The solid with cross-sections are the equilateral triangle over an interval [0,2] on the…

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: Find the area bounded by the circle x² + y² = 25, the x-axis and the parabola x² - 2x = y.

A: Equation of Circle is x2+y2=25  Centre of Circle = (0,0) Radius of Circle = 5 unit Equation of…

Q: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

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

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: Find the area lying between the parabola y = 4x – x² and the line y = x -

A:

Q: A\ Calculate the area of the segment cut from the curve y =2x2 by the line y = x+1 with x2 0.

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.…

A:

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

A:

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

A:

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 approximate area between the curve Ax) = -4x + 32x and the x-axis on the interval [0, 8]…

A:

Q: Use inscribed and circumscribed rectangles to find the area of the region to the right of the line x…

A: Concept: the area between the region y=f(x) and ==g(x) on the interval [a, b] Let us assume that…

Q: Find the number b such that the line y = b divides the region bounded by the graphs of y = 9x2 and y…

A: To find the number y=b that divides the region bounded by the graphs of y=9x² and y=16 into two…

Q: The area bounded by the curves: у-х, у-6-х аnd у-0.5х is:

A: see below the answer and explanation

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: 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: The area of region bounded by the parabola y? = 4x and the line y = 2x – 4 is

A: In the given question, the concept of integration is used to find the area of the common region.…

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: Find the area of the region bounded by the line y = 2x – 5 and the parabola y = x² – 4x. - -

A: Graph of enclosed region -

Q: Find the area of a triangle bounded by the yy-axis, the line f(x)=10−2xf(x)=10−2x, and the line…

A: Now, from the graph we have the points of intersection of the lines

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

A:

Q: Find area bounded by the circle x² + y² = 25, the y-axis and the parabola y = 6x - x².

A: Circle: x2+y2=25 Parabola: y=6x-x2 To Find: Area bounded by the circle, the y axis and the parabola…

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.