Find the area below f(x) = -x + 4x + 3 and above g(x) = -x' + 7x² – 10x + 5 over the interval 1

Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

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

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Q: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

A: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

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 region between the graphs of y = 20 - 2² and y=-2x - 15 over the interval 6 < x…

A: Please see the below picture for detailed solution.

Q: 4. Find the area of the region bounded by the graphs of y = x3 + 6x, x = 0, x = 2, and the x-axis.

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Q: Shade the area of the region bounded by, x² + y2 < 7² and |x| + |y| 2 7 Hence, find the area of the…

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 10x, y = 0

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Q: Sketch the region bounded by the graphs of the equations f(x) = x2 + 2x, g(x) = x + 2 and find the…

A: The region bounded by the graph is as below

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

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

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Q: Find area of the region. f(x)=x2-8x g(x)=0

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Q: Find the area of the region between the curves y = x x-1 and y =-2x+2 from x = - 1 to x= 1.

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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: ) Find the area of the region bounded by the lines ( yı=x² ) & (y2=2-x) for x<0.

A:

Q: Shade the area of the region bounded by, x2 +y2sp2 and |x| + |y| 2p Hence, find the area of the…

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Q: Sketch the graph of the curve y z (x-6)(x-7)(x-8) Shade the area of the region bounded by the curve,…

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Q: Find the area bounded by x2- 6x +y = 0, x² - 2x - y = 0. and the x-axis.

A: We have given two curves;

Q: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

Q: Given y = 3x –- 2x +1, y =-x² + 2x +1 and a straight line y = 0.5x ; where x>0, 1. Sketch the curves…

A: Given y=3x3-2x2+1  , y=-x2+2x+1 and a straight line y=0.5x. We need to : 1) Sketch the curves and…

Q: Find the area bounded by the curve y = 4+2x+z² and x-axis from z=-3 to z = -1. Area of the region -

A: Given query is to find the area of the region bounded by y=4+2x+x2  and x-axis from x=-3 to x=-1

Q: The area of the region bounded by the curve y= e", the x-axis,'the y-axis, and the line x 2 is equal…

A: We have to find the area of the region bounded by the curve y=e2x , the x-axis, y-axis and the line…

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

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

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Q: Find the area of the region under the curve y = 6x² + 4x + 5 from x = -1 to x = 2.

A: Solve the following

Q: Find the area of the region bounded by the lines ( y=x2 ) & (y=2+x) for xs 0.

A:

Q: Sketch the graph of the curve y (x-p)(x-p-1)(x-p- 2) Shade the area of the region bounded by the…

A:

Q: The area of the region between the curve y x'-6x+ 8 and the x-axis & x=0; x= 3 is given by -6x+8)kke…

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Q: The area of the region bounded by the curve y= x3−3x2−x+3 and y=0 is

A:

Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: What is the area of the region between y = x - 2x- 3 and the x-axis from X = - 2 to X = 0?

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Q: solve the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4

A: To find out the area bounded by the curves.

Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

Q: Find the area between the curve x = y2 and the line x = y + 2 Solution : * with respect to x:

A: Given curves x=y2. . . . 1x=y+2. . . . .2 Equating (1) and (2) y2=y+2y2-y-2=0y-2y+1=0y=2,-1

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: What is the area of the region between y=x^2-2x-3 and the x-axis from x-0 to x=6?

A: Given,      y= x2-2x-3and the x-axis  from  x=0 to x=6.

Q: Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2&lt;= x &lt;=2 of…

A: Find the area bounded by curves

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

A: Given:       region y=x+6                 f(x)=x+6                 y=x2                 g(x)=x2…

Q: Sketch the region enclose by y=x2-9x+21 and y = -x2+11x-27. Decide whether to integrate with respect…

A: Given data is : y=x2-9x+21 and y=-x2+11x-27  To sketch the region.

Q: Find the area of the region between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

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Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

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: What is the area of the region between y =x-2x-3 and the x-axis from x=0 to x-9?

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Q: Find the area of the region bounded by y = (1/8)(-x2 + 6x + 7) and y = -6.

A: Solved below

Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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Q: Find the area under the curve f(x)=x3f(x)=x3 on x=[−2.5,3.5]x=[-2.5,3.5] using the Midpoint Rule…

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.