Q2) Find the area of the region bounded by the (y=V4+x ), (y;=2-x) & ( y;=1).

Q: Find the area of the region bounded above by y AY -x² + 8 and below by y = x². ==

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Q: find the region bounded by x= Y-y3 ,X=1 = 1 Y=L, revolved about o X- axis

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the area A of the region between y = 4x2 + 10 and y = 2x + 7 over the interval [-3, 2].

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Q: y = 2 – x2 ; y =-x

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Q: Find the area of the reglon bounded by the graphs of the equations. y = -x+ Bx, y = 0

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Q: Find the area of the region. 5ex y = 1 + e2x y 4 3 x = In V3 2 1 -2 -1 2)

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Q: Sketch the bounded region enclosed by y=e^5x, y=e^6x and x=1. Decide whether to integrate with…

A: Sketch the bounded region enclosed by y=e^5x, y=e^6x and x=1. Decide whether to integrate with…

Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: B. Find the area of the region bounded between the curves y = Vx + 3, y (x+ 3)/2

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Q: 29. Find the area of the region bounded by y =. = x2 + 3x + 1 and y = 6x - 1. [4.4]|

A: If two curves f(x) and g(x) defined over the interval [a,b], then the area bounded by the curves…

Q: Find the area of the region bounded by y² = 4ax and x² = 4ay.

A: We have to find the area of the region bounded by y2=4ax and x2=4ay.

Q: R is the region bounded by y = 4 – x2 and the x-axis and it is revolved about y = 4.

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Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: The region R is bounded by y 4 %3D and y = x +3. -

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Q: The area of the region bounded by y=x2+2, y=−x, x=0 and x=1 is

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Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: Find the area of the region bounded by the graphs of the equations y = e, z = 0, z= 5, y = 0

A: To find the region bounded by the following graphs of equations,  y = ex  x = 0 x = 5 y = 0

Q: Find the area of the region bounded by one loop of the curve x2 y*(1 – y²) %3D

A: The curve is given as , x2=y41-y2 The graph of the curve is

Q: The volume of the region bounded by x² + y² + z2 =1 is

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Q: Find the area bounded by y = X = 0, y = 0, and x = 3. V49-16x2

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Q: Find the area of the region bounded by the graphs of the equations. y = Vx(1 – x), y = 0

A: we have y = x(1-x) clearly x≥0we find area of the region        y≥0 if 0≤x ≤1and  y≤0 if x≥1…

Q: y =-z +4x, y= 0

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Q: Determine the area of the region bounded by x = y² – y – 6 and 2y + 4.

A: According to the fundamental theorem of calculus ∫abf(y)dy=F(b)-F(a), where dFdx=f(x). The equation…

Q: and the y-axis. 2. Evaluate , 5x³ cos(y³) dA, where D is the region bounded by y = 2, y =:

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

Q: 3. Determine the area of the region bounded by y = 2a2 + 10, y = 4r + 16, r -2andr = 5. %3D

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Q: Find the area of the region bounded by y = 5-x2, y 2x+2, y=-x-1, a. in terms of x b. in terms of y y…

A: We will find out the required value.

Q: Find the area of the region enclosed by x = y3 and x = Vy - 6.

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Q: Shade the area of the region bounded by, x 2+ y2sp? and |x| + ly| 2p Hence, find the area of the…

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Q: 2. Find the area of the region bounded by x=y², x=-1, y = 2 and y = -1.

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Q: 2. Find the area of the region bounded by y = 1- 2x² and y = |x|.

A: The area under a curve between two points can be found by doing a definite integral between the two…

Q: Solve for the area of the region bounded by: x^2 = 4y + 4 and x = y - 2

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Q: Find area of the region bounded by x2 + y2 = 32, 6y = -6x and 20y = 6x where y 2 0. Leave your…

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Q: Find the centroid of the region bounded by the graphs y=6– x² and у %33 — 2х.

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Q: Find the area of the region bounded by y = 5-x2, y 2x + 2, y=-x-1, a. in terms of x b. in terms of y…

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Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: Find the area of the region bounded by the graphs of y = x2, y= x² – 2r +3 and y= 2x- 1.

A: Given curve is y=x2, y=x2−2x+3 and y=2x-1 we have to find the area of the region bounded by the…

Q: y = 2x 2 − 8x + 12 and y = −2x + 12.

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Q: 2. Find the area of the region bounded by x = y² - 4 and x = 3y.

A: Given query is to find the area of the region bounded by x=y2-4 and x=3y. The rule for integration…

Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: Determine the area of the region bounded æ = y2 – y – 6 and a = 2y + 4.

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Q: Q1: Find the area of the region bounded by y= Vx, y v4-x and x-axis.

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Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x², and bounded on the…

A: We need to calculate the intersection points of the given curves. So,…

Q: y=√x, x = 4, and the x-axis.

A: Consider the given function y=xand the x-axis

Q: Find the area of the region enclosed by the curve y=x2-2 and by the line y BO 2. y=x²-2 y=2 Co

A: The equation of the curve is:                                            y=x2-2  The equation of the…

Q: While evaluating the area of the region bounded by two curves V/y = x and y – 10x + 21 = 0, the -…

A: We will find interesting points.

Q: Solve the area bounded by y³+y²+10 = (x+1)², the lines y=−2 and y=2 *

A: The given problem is to find the area bounded by given region and between the given lines y=-2 and…

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.