Find the exact area of the region enclosed by the graphs of x = 9- y2 and x = 7. You must show on your work, how you got the bounds and also the Fundamental Theorem of Calculus.

Q: Find the exact area of the region enclosed by the graphs of x = 8 – y2 and x = 3. You must show on…

A: we have to find the area of the region

Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 4x, y = 0

A: We first find where the two equations meet.  We plug y=0 in the first equation and find x

Q: Find the area of the region bounded by the graphs of y = x2 – 6 and y – 3 = 0. %3D

A: Given: Two curves y=x2-6 and y-3=0

Q: Find the area of the region bounded by the graphs of the equations. y = 4x + 2, x = 0, x = 2, y = 0

A:

Q: Find the area of the region bounded by the graph of y = x /(x2 + 1) the x-axis, and the line x = 3

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Q: Find the area of the region bounded by the graphs of the equations. x = 1, x = e, y = 0 y

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Q: Find the area of the region bounded by the graphs of the equations y=x−x3, x= 0, x= 1,and y= 0.

A: Given equations: y=x-x3x=0x=1y=0 The region bounded by the graphs is shown below:

Q: y = 4Vx +. 1 y = 0, x = 1, and x = 9

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Q: 3 y = x° + x and y = 3x² +3x for x 2 U.

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Q: 3 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

A:

Q: Find the area of the region bounded by the graphs of the equations. y = 3 + Vx, x = 0, x = 8, y = 0

A: try to draw the curve first.

Q: Find the area of the region bounded by the curves y = x ^ 3 - 12x, y = x ^ 2.

A: y = x ^ 3 - 12x, y = x ^ 2.

Q: Find the area of the region bounded by the graphs of the equations. y = 4 + Vx, x = 0, x = 8, y = 0

A:

Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

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Q: Evaluate the area of the region bounded by x=y^2 and y^2 = 6-x

A: To find the area

Q: Find the area of the region bounded by the graphs of the equations.

A: If there are two curves given,say, f(x),g(x) over an interval [a,b] such that over this interval…

Q: Find the area bounded by the graphs of y = 3x2; x = 0; x = 2; and the x axis.

A: Given,

Q: Find the area of the region bounded by the graphs of the equations.                   y = −x2 + x +…

A: we have to find the area of the region bounded by the graphs of the equations: y=-x2+x+6y=0 as we…

Q: Determine the area of the region bounded by x=--y2  +10 and x=(y -2)2

A:

Q: Find the area of the region bounded by the graphs of the equations.                y = x − x3,    x…

A: The graph of bounded region by the curves y=x-x3, x=0, x=1, y=0:

Q: Find the area of the region bounded by y = ¾(x + 2), x = 2 and the x-axis.

A:

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A:

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

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Q: Find the area of the region bounded by y = 9x + 8, y = -3x + 4 and x = 14. Leave your %3D answer…

A: Area between curves

Q: Find the area of the region bounded by the curves x-y+ 4y = 12x, x = 1, x = 4, and the x-axis %3D

A: First we will draw the graph  and we will find the area by using following formula Area A = double…

Q: Find the exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

A:

Q: Find the area of the “triangular” region bounded on the left by x + y = 2, on the right by y = x2,…

A: Graph the given equations first.We have to find the area of the shaded region

Q: Find the area of region bounded byf (x) = 8 – x², g(x) = 2x , from x = 0 and x = 2. Show all work.

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

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

A:

Q: Find the area of the region bounded by the graphs of the equations. 9 x = 1, x = e, y = 0 x

A:

Q: Find the area of the region bounded by y = x; y 8-x' and y 4x +12.

A: It is given that, y=f1(x)=4x+12,y=f2(x)=8-x2,andy=f3(x)=x2 Area under the bounded region can be…

Q: determine the area of the region bounded by x= |y| and x=2-y2

A: determine the area of the region bounded by x= |y| and x=2-y2

Q: What is the area of the region between the graphs of y=x^2 and y=-x from x=0 to x=2?

A: The equation of the curves are : C1 : y = x2C2 : y =-xC3 : x = 0C4 : x = 2 To evaluate : The area of…

Q: Find the area of the region bounded by the graphs of the equations. y = 2+√√x, x = 0, x = 8, y = 0

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Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

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

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Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y – 3 = 0. - -

A: Graphically: Now, the area can be found as the following.…

Q: Find the area of the region bounded by the graphs of y = x +6x, x = 0, x = 2, and the x-axis.

A: Answer

Q: What is the area of the region bounded between the graphs of x= y + 1 and x = 3 – y? ?

A:

Q: Find the exact area of the region enclosed by the graphs of x = 9 – y and x = 4. You must show on…

A: Given: x=9-y2 and x=4. Let fy=9-y2 and gy=4.   Plot both the equations.

Q: Find the area of the region bounded by the graphs of the equations.                 y = 2√x − x,…

A: Given: The equations, y=2x-x and y=0.

Q: Find the area of the region bounded by y = x2 - 4x + 3 and y= -x2 + 2x + 3. Set up

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Q: Find the area of the region bounded above by y = x^2 + 1, bounded below by y = x, and bounded on the…

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Q: Find the area of the region bounded by the graphs of x = 3-y^2 and x = y+1

A:

Q: Find the area of the region bounded by y=-x^2+3x+1 and y=-x+1

A: Please see the diagram below to understand what's going on:

Q: Find the area of the region bounded by the curves y= x2 x3−3x and y= 1 x3−3x on the interval…

A:

Q: What is the area of the region between the graphs of y = x3 and y = -x from x = 0 to x = 2

A: Area between curves

Q: Find the area of the region bounded by the graphs of the equations.                    y = 1 + 3√x,…

A: Solution: Consider the given equations  y=1+3xy=0and x= 0x =8 First of all, draw these equations and…

Q: Find the area of the region bounded by the curves y = x +2x and y=-x² +4.

A:

Q: Sketch the region bounded by the graphs of the equations and find its area. y =x² +1; y=x+1

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.