11. Find the area of the region between the function (*) = x' –x+2 [-1,2]. and the x-axis on the x-interval y= Vx-10 y = 0 12. Find the area between and between x =0 and x =9. 13. Find the area bounded by these two curves: Y =9-x² and 2y = x² -3x +12 14. Find the area of the region bounded by these two curves: x = y – 2y and *-y-4=0_

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

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Q: Find the area between the curves. y = x2 − 2x + 7 and y = x2 + 8 from x = 0 to x=6

A: Let fx=y=x2-2x+7 and gx=y=x2+8. First, we will find the intersection point of both the curves…

Q: 6. Find the area between the curve y = x(x - 3) and the ordinates x = 0 andx = 5.

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Q: 3. Find the exact area between the curve f (x) = -2x² + 12x + 7, the x-axis, and x=1 and x=5.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

Q: 1. Find the area bounded between the curves: y = x+1, y = -2x + 7 and x = 0 A. With respect to the X…

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Q: 5. Find the area between the curve y, =x² - 4x +12 and y, = x² from 0<x<4

A: Given curves are y1=x2-4x+12y2=x2 Also 0≤x≤4

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: 4. Find the area bounded by the curve a²y = x³, the x - axis, and the line x = 2a. Solve in two…

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Q: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

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Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: Find the area between the curve y = x² + 7x + 12 and the x-axis from x = -3 to x = -1. Step 1 Notice…

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Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: 1. Find the area of the region bounded by the ves y = x³ – 5x + 6, y = 10 – 4x – 4x2 and the line x…

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Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

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Q: 8. Find the area under the curve y = e* and above the x-axis from x = 0 to x=1. -3x

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Q: If L2 is the sum of the approximating rectangles for the area under the curve y = | cos x| from 2n…

A: Solve the following using left end points approximation

Q: The area under the curve y = Vĩ bounded from below by the 16 x-axis and on the right by x = 4 is…

A: Integration can be used to find area of region bounded by a set of functions. For two functions…

Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: What is the area bound between the curve y= \x/2 and the x-axis between x =-3 and 4/2 - 2/3 3 x = 2?…

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Q: 8. Find the area between the curves y = x x² and y = x2 – 4x between x = O and x = 2.

A: For calculating the area between curves first of all we will draw the schematic diagram of the…

Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the area under the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

Q: 2 (F(x) + x³)dx = ? %3D -1

A: Given that the area under f(x) in [-1,2] is 10br2 So,

Q: 1. Solve the area bounded by the curve (x - 2)² = - ( y - 4) and the lines x=- 2 and y= 4.

A: The area bounded by the curves (x-2)2=-(y-4) ,x=-2, y=4 is as shown above.

Q: A population of E. coli bacteria will grow at a rate given by w'(t)=(3t+2)^1/3 where w is the weight…

A: Given :- A population of E. coli bacteria will grow at a rate given by w't = 3t+213  where w is the…

Q: (5)Obtain the integral curve for x 2+y = x passing through the point

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Q: 1. The area bounded by the curves y x2,y 0, x = 2,x = 5 is 39. 2 is 10

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Q: Find the area of the region enclosed by the curves f(x) = 7x + 1 and g(x) = 5x + 17, and the lines x…

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Q: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

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Q: Can i get help step by step?

A: We graph y=7x using a graphing calculator  The graph cuts  x-axis at x=0  So over the interval…

Q: 1. Find the area bounded by the curves y = 3x'+1 x=0 y= 3x+1 x-1 А. 3/2 5 В. 3/4 2 С. 1/4 -2 -1/0 21…

A: y = 3x3+1 , y = 3x + 1

Q: Let f(x) 4x³ and g(x) = sin (Tx) and R is the region bounded by the two %3D functions on the…

A: The slope of a tangent to a curve at a point is obtained by calculating the derivative of the curve…

Q: - 5. Find the area bounded by the curve y² − 3x + 3 = 0 and the line x = 4

A:

Q: 4. Use the right-endpoints and 3 subintervals to approximate the area of the region under the curvey…

A: Given curve is y=1/x We will divide the interval [1,4] into three sub-intervals. The length of each…

Q: 2 Set up the definite integral required to find the area of the region between the graph of y = 20 –…

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Q: 11. Find the area bounded by the curve y² + 2x - 2y - 3 = 0 and the y-axis.

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Q: 3 Find the area under the curve y over the interval [3, 8] (4x + 2)?

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Q: Find the area above the curve y=Inx in the lower half-plane between x=0 and x=1. YA y=In x 1

A: The correct option is option d. From the curve determine the upper curve , lower curve. and the…

Q: 1. Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: 1. Find the area of the region bounded by the curve y = f (x) = |a² – 4| and the lines x = -3, and x…

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

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Q: 19. (a) Find the area bounded by the curves y = 2x2 and y = 4x. (b) Two cars both start on a journey…

A: Given two functions: y=2x2 and y=4x To find a) Area under the two curves b) If two curves represent…

Q: Consider the graph of y 2Vx between x 0 to x 9 and the graph of the vertical line x= 9 as shown…

A: Given that:

Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…

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.