Identify the radius and height. The region bounded by y x and the x-axis, -2

Q: 9. y = x²; y = 8-x²; y = 4x +12 %3D

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Q: Find the area of the region bounded by y=0 and y = -5x + x° 47 42 37 42 57 21 57 42 37 21

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Q: nd the area of the region enclosed by the curves x = 5y, x 0, and y = 1.

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Q: Find the area of the region enclosed by the given curves y = x^2 y = 32/ x^2 + 4

A:

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

A: Given: y=2x-6x=0 and x=4

Q: Find the area of the region enclosed by the graphs of: y? = 15 – x and x = 6. %3D

A:

Q: Find the area of the shaded region. y y= v x 1 1, 1) X= 27 1 y = 10 15 20 25 2. 4.

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

Q: Consider the infinite region in the first quadrant bounded by thegraphs of y = 1/x2 , y = 0, and x =…

A:

Q: Find the total area of the region enclosed by the curve x = y^(2/3) and the lines x = y and y = -1.

A: To determine the area bounded by the curves.

Q: Find the area of the shaded region. y y = Vx 3 마1, 1) x = 27 1 y = X 5 10 15 25 20 2.

A: The area under the graph can be determined by integration. Let, Boundary points are, x1=1 and…

Q: Find area of the region under the curve - 2 y = and above the x-axis, for 9 < r<11. area =

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Q: What is the area of the region enclosed by the curves y = x³ and x =y² ? A) B) D) E) 15

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Q: Q3) Find the area of the region enclosed by the curves: y y = x, and y = 1

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Q: Find the area of the region enclosed by the graphs of 1 0, and x = 10 1 y = 0, x 1 — 25л2 NOTE:…

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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 region bounded by the line y=(1/2)x and the parabola y? = 8-x.

A: Area between curves

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

A:

Q: The region enclosed by x = y1/3, x = 0, y = 27

A: Find the volume

Q: Find the area of the region enclosed by the curves y=x2−1 and y=8.

A:

Q: Find the exact area of the region enclosed by a = t - 9t and y = 4t/2 and the y-axis. Be sure to…

A: To Find: The area of the region enclosed by x=t2-9t and y=4t1/2 and the y-axis.

Q: Find the area of the shaded region. y 4 3 y= V x 2 마 1, 1) X = 27 y : to 5 10 15 20 25

A: The sketch of the region bounded by the curves is  To evaluate: The area of the shaded region.

Q: Find the area of the region enclosed by the graphs of 1 1 =0, and x = 4 y = 0, x V1– 4x? - NOTE:…

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Q: Consider the infinite region in the first quadrant bounded by thegraphs of y = 1/√x, y = 0, x = 0,…

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Q: Shade the area of the region bounded by, x² + y? p

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Q: Find the area of the region bounded by the following curves. y  =  x2 + 4x,     y  =  160 − x2

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Q: Find the area of the shaded region: 1. yA x= 2 2, 4) y= x? y= 0

A: We will find the area of shaded region as following.

Q: Find the area of the given region.

A: Integration is used to find the area under a curve. So, on integrating the function y=x-x2 from x=0…

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: Find the area of the shaded region. y x= 2 y = 2 e* y= 5 x– 1

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Q: Find the area of the region enclosed by the graphs of 1 y = 1 y = 0, x = 0, and x = V1 – 16x2 NOTE:…

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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: Determine the area of the region enclosed by the curves y=1/x, y=1/x2, and x=9.

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Q: Graph the region bounded by the curves and determine the area of the region. x = y? – 2y; x = 0

A: ANSWER :

Q: Find the total area of the region between the curve and the x-axis. 9) y = (x + 4)3; 0 <x<3

A: The Area Under a curve The area under the curve between two points can be found by a definite…

Q: 10. y = x; y = x'; x+ y = 2

A: Function is the unique relation, where each x is mapped to unique y. It can be of many type,…

Q: Sketch the region enclosed by the given curves and find the area. x = 2y ² ,  x = 4 + y

A: Sketch the region and integrate in y variable.

Q: For each problem, find the volume of the solid that results when the region enclosed by the curves…

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Q: Find the area of the shaded region. y y = x 2 11, 1) X= 27 1 y= 5 10 15 20 25 3.

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Q: Find the area of the region enclosed by the curves y = x2 – 4 and y = 5. The area of the region…

A: area of the region enclosed by the curve is 36 detailed solution is given below

Q: Let R be the region enclose by the graphs of y=lnx, the line x=3, and the x-axis. Calculate the…

A:

Q: Find the area of the region enclosed by the graphs of 1 1 y = V1 – 4.x2 y = 0, x = 0, and r 4 NOTE:…

A: Given y=1/√(1-4x2) ,y=0,x=0 and x=1/4

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: Identify the radius and height. The region bounded by y = x and the x-axis,-3 <x<2, revolved about x…

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Q: Using your previous work, find the region bounded by the curves y = x² and y = x³.

A: Given that, There are two curves following, y = x2  and   y = x3 We have to find the area bounded by…

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

A: The curves are given as , y=11-9x2 , y=0 , x=0 , x=16 Find the area of region.

Q: Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and…

A: Area bounded by the curve y=x2 and the line y=2-x

Q: Q8 Find the area of the region enclosed by the curves: y = x³, y = x, x > 0.

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Q: Find the area of the region enclosed by x = y' and x Vy- 6. Answer:

A:

Q: Find the area of the region enclosed by the following curves y%3Dsec" x, y3Dtan x, X= and x= 6. The…

A: We can represent this area on the graph

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.