Use the grid to estimate the area of the region bounded by the curve shown in the figure, the horizontal axis, and the vertical lines x=−5 x=−5

Q: Sketch the region and determine the area of the region in the first quadrant bounded by f(x) = the…

A: We will sketch the region using a graphing calculator  f(x)=(6-x)/x (red) x=2 (blue)

Q: Find the area A of the shaded region where b = 9. y = |x| + -b A =

A:

Q: Find the area of the region enclosed by: y = x³ and Y = = x4

A: Given curves are  y=x3 and y=x4 Point of intersection of the curves are obtained as follows.…

Q: Find the area of the shaded region. y 2+ y = x+ – 2x3 1 y = 0 2 -1 i

A: Given, The function  ; y = 0   and  y = x4 - 2x3  the limits : x = 0  and x = 2 We have to find the…

Q: Find the area of the shaded region. x = 2- y2 -2 2 11 A 10 - 3. 8. D. 3. 2.

A: The area of the Shaded Region: the shaded zone's area is computed by subtracting the area of a…

Q: Find the area bounded by the curves y=8x-x2 and y=x2, and the line 4x-y=-12.

A: I have appended the formula used in the solution part.

Q: Find the total area of the region between the curve and the x-axis. 24) y = x2(x- 2)2; 0sxs2 15 A) -…

A: The graph of the bounded region is as shown above. As shown draw a stipe parallel to y-axis. So, y…

Q: Find the area of the region between y = x2 and y =  -x2 + 18x.

A:

Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: Q5 (a) Find the area of the region enclosed by the lines and curves, y=x' -2,and y =2

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

Q: Q2 a) Find the total area of the region enclosed by the curves in below figure: (-2,8) y-axis (2,8)…

A: Given problem is :

Q: Find the total area between the region and the x- axis. y = x3 – 3x? + 2x -1 sxs2

A: Consider the curves, y=x3-3x2+2x  ;       -1≤x≤2

Q: A y y = x2 + 1 y = x -1 2

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Q: Find the area of the region enclosed by the parabola x² and the x-axis. Y = 10x AREA :

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Q: Find the area of the shaded region. y = x² +1 %3D 5 y = x -1 A 23 2. 2/2

A: Given

Q: y = \x| -1 and y 3 3

A: First break the modules function then draw the curves and find the area.

Q: Find the area of the shaded region.

A: Given the polar curve r=θ

Q: Find the area of a triangle bounded by the y axis, the line f(z) 1 z, and the line perpendicular to…

A: Area of triangle = (1/2)*base*height

Q: Find the area of the region(s) enclosed by the curve (x) the x-axis, and the lines x = -1 and X= 2.…

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Q: Find the area of the region enclosed by these graphs and the vertical lines x = 0 and x = 3. square…

A: The given function is, fx=-x2+2x+4 and gx=-x+4 To sketch the function. To find the area of the…

Q: Find the total area between the region and the x- axis. y = x3 – 4x ; -2<x<2 -

A: Given: y=x3-4x The graph of the given function is,

Q: Find the area of the shaded region. r = ve

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Q: Sketch the region enclosed by y = 3x and y = 5². Find the area of the region.

A: find intersection

Q: y=x 2 y = x+1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the area bounded by y= (11 - x)1/2, the lines 3x = 2 and x = 10, and the X-axis. 19.456 sq.…

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Q: Find the area of shaded region frx)- メ+3 grx)= -x²_ 3 Alx) 3 gre a) 176 3 5) = 88 C) 44 3.

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Q: Find the total areas of the shaded regions

A: according to given figure areaA of shaded region is given by A=∫01x13-x12dx…

Q: y = xe¯,y = x + 1, x = 2, and the y-axis.

A: lets plot the graph of the given functions

Q: Draw the figure showing the region and find the area of the region bounded by the curves. y = 4x –…

A: Area of the region is obtained by definite integral . There are two ways of finding area , first…

Q: Find the area bounded by the line x – 2y + 10 = 0, the x-axis, the y-axis and x = 10. A. 75 В. 100…

A: SOLUTION-

Q: b) Find the exact area of the region enclosed by the curve y = x² – 3x, the x-axis and the vertical…

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Q: b) Find the area of the shaded region. 1) ii) アー =-y 2Fx=2-

A: 1. Required area is, ∫04x dx+∫04-14x dx=∫04x12 dx+14∫04x dx=x323204+14x2204=23432-0+148-0=238+2=223

Q: y = x(x2 – 4)

A: We have to find the area of the shaded region.

Q: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

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Q: Find the area bounded by the given curves. y = x2 − 1 and y = 8 − 8x2        square units

A: Given :

Q: b) Find the total area between the region and the x- axis. y= x – 4x ; -2<x<2

A: Given equation is                    y=x4-4x

Q: Find the area of the shaded region. x = -y 2 x = 2 - -2 A B 10 3 2.

A: Given query is to find the area of the shaded region.

Q: Determine the area enclosed by the curve r² = 4a²cos3θ a. 4a² b. 8a² c. 16a² d. a²

A: To find the area enclosed by the curve r2=4a2cos3θ

Q: Find the area of the shaded region. 5ft

A: Given shaded region is  This shaded region is quarter of a circle having radius 5 ft. Therefore the…

Q: ind the area of the region bounded by the x-axis and the lines x =- 2 and y 4x + 20.

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Q: Find the area A of the shaded region where b = 7. y = |x| + -b

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Q: Sketch the region enclosed by y = 7x and y 87². Find the area of the region. =

A: Area of the region enclosed

Q: Find the area of the shaded region (using the area between two curves). y=x2 - 4 y=2x² •x - 6

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Q: Find the area of the region in the first quadrant bounded by the line y=5​x, the line x=5​, the…

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Q: Find the area of the region enclosed by the curves y = 2 - x² and y = x. (a) (c) 9 2 54 (b) (d) 40 7…

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Q: Find the area bounded by the curve y=-x³x² + 3x and the line y=x. 16 A 8 square units B 16 square…

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Q: Find the area of the region enclosed by these graphs and the vertical lines x = -1 and x = 0. |…

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Q: problem in photo attached

A: Given that the curve is bounded by the curve x = y2 – 2 to x = ey and y = – 1 to y = 1.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

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.