Find the area of the region bounded by the graphs of the given equations. y=1-x²,y= 1-4x The area is . (Type an integer or a simplified fraction.)

Q: Find the area of the region blinded by the graphs of the given equations. y=6x, y=x2

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Q: 1. Find the area of the region R (shaded region). a) y =x-2x+ 2 R

A: Area under the curve is nothing but the Definite Integral with limits being the initial and final…

Q: Find the area of the region between the graphs of y = 16 – x² and y = - 3x – 24 over the interval –…

A: The objective is to find the area.

Q: 3. Find the area of the region bounded by the graphs of the given equations. 2 y = 4x, y = x? The…

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Q: In the given question , sketch the region bounded by the graphs ofthe equations and find the area of…

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Q: Find the area of the region described in the following.   The region bounded by y = x2 - 2x + 1 and…

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Q: Find the area of the region enclosed by the graphs of x = y2 and y = x - 2

A: Ans: Given curves    x=y2, x=y+2

Q: Find the area of the region bounded by the graphs of the equations: x = 4 – y? x = y – 2

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Q: In the given question , find the area of the region bounded by the graphs of the equations:-   y = 1…

A: Given : The equations y = 1 - x4 , y = 0 .

Q: In the given question , find the area of the region bounded by the graphs of the equations. y = -x2…

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Q: Let b 1 be an integer. The area of the region bounded by the graphs of the functions y = 20bx and y…

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Q: Find the area of the region bounded by the graphs ofy = x² - 4 and y =r+2. Give your answer as a…

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Q: x2 – 7x + 20 and Find the area of the region bounded by the graphs of the functions y = y = 2x + 6.…

A: Given, Functions  y =x2 -7x+20  and y =2x+6 We have to find the area of region bounded by the graphs…

Q: Find the area of the region enclosed by the graphs of 1 1 y = 0, x = 0, and x /1 – 4x²' NOTE: Enter…

A: First set the integral for area and the using rule of integration solved it.Final solution is in the…

Q: 6. Find the total area between the region and the x-axis y = -x² – 2, –3 < x < 2 %3D

A: Find the zeroes of the function as follows. y=0-x2-2x=0x-x-2=0x=0, x=-2  The zeros divide the…

Q: Find the area of the region between y² = x and x = y +2.

A: Given,  y2 = x   and  x = y+2  We have to find the area of region between y2 = x   and  x = y+2

Q: Find the area of the region described in the following. The region bounded by y = 4x + 4, y = 6x +…

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Q: Find the area of the shaded region. y =x4. 32 -2 -5- -10+ -15+ -20- 30+ 35- 40- y = -x 4 O 256 516…

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Q: 20-21. What is the area of the region between the graphs of y=-x² and y = -x? A) B) D)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: y x-3' y = 0, x = 4, аnd x = 3 + e

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Q: (4) Find the area of the region in the first quadrant bounded above by y = √x - 1 and y = x - 3.

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Q: Find the area of the region bounded by the graphs of the given equations. y =– x- 3' y = 0, x = 4, x…

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Q: Find the area of the region bounded by the graphs of the given equations by partitioning the y-axis.…

A: Given equations: y=lnxx=ey=0 Its graph:

Q: Question: a) Find the total area between the region and the x- axis. y x-3x2 + 2x -1<xs2

A: To determine the total area of any curve: Draw the curves Determine the bounded region. Now, using…

Q: Find the area of the region enclosed by the graphs of 1 1 y = 0, x = 0, and x = %3D V1- 9x2 NOTE:…

A: Using formula of area under the curve.

Q: Find the area of the region enclosed by the graphs of the given equations by partitioning the…

A: Given: y=x, y=x3, about x-axis

Q: Find the area of the region between the graphs of y = 16-2² and y = -4≤ ≤ -1. The area is 2x+8 over…

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 2x, y = 0 Submit…

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Q: Find the area of the region bounded by the graphs of the given equations.   y = 3x + 18 , y = x 2.

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Q: Find the area of the region described in the following.  The region bounded by y =  6x and y = 3x2 -…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: x and y -2x Find the area of the region enclosed by y

A: Solution is given below:

Q: 3. Find the total area between the given region and the x-axis .2 a) y = -x - 2x,-3 < x < 2 b) y =…

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: Find the area of the region enclosed by the graphs of 1 1 y = 0, x = 0, and x = 8. || /1 – 16x²…

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Q: Find the area of the region described in the following.  The region bounded by y = x3 and y = 9x

A: It is given that, the region bounded by y = x3 and y = 9x We have to find the area of the region.

Q: Find the area of the region enclosed by the graphs of x = y³ - 14y and y + 3x = 0.

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Q: of the given equations. y = x² - 2x - 24, y = -x² 1

A: Given curves are      y=-x2             . . . (1)    y=x2-2x-24  . . . (2) The graph is given be

Q: Consider the following equations. Y= (1)/ (x2 + 1), y=0, x= -1, x= 1 Sketch the region bounded by…

A: Here given curve is Y = 1/(x2 + 1) Y = 0 X = -1 X = 1

Q: Find the area of the region described in the following.   The region bounded by y = 3x - x3 and y =…

A: Find the area of the region described in the following.   The region bounded by y = 3x - x3 and y =…

Q: Find the area of the shaded region. y 3- x= y - 6 y = 1 (x = e' -2 2 4 H y = -1 2. 2. 3.

A: Consider the graph

Q: Find the area of the region bounded by the graphs of y2 = 5 – x and y2 = 4x.   Please put a…

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Q: 8. Find the area of the region bounded by the graphs of f(x) = 6x – x² and g(x) = x² – 2x A. - 64 B.…

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Q: 10 2. Find the area of the region enclosed by y = 2x – x² and y = -3.

A: Given curves, f(x)=y=2x-x2 g(X)=y=-3

Q: Find the area of the region bounded by the graphs of the equations. y = 5 + √√x, x=0, x=8, y = 0 59…

A: Given below figure is the required region whose area to be find.Area of teh region is calculate by…

Q: Find the area of the region bounded by the graphs of the given equations. y = - 2x-x, y= - 8 The…

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Q: Find the area of the shaded region. y 3- x = y - 5 y = 1 x= e -6 -4 -2 2 4 y = -1 2 3

A: Subtract the red function from the blue function and integrate between the limits -1 and 1 with…

Q: Find the area of the region between y2=x and x=y+2

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given by…

Q: Find the area of the region enclosed by y = 4 – x², y = -x+ 2, x = -2, and x = 3.

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Q: Find the area of the shaded region. y 3- x = y - 2 y = 1 x= e X -3 -1 (1 2 3 4 y = -1 -2

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Q: Find the area of the region bounded by the graphs of the given equations. y = 1-x, y = 1-4x

A: Given: Equations: y = 1-x2, y = 1-4x To Find: Area of the region bounded by the graph of the given…

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.