Find the area of the region bounded by the curves y = x2 – 12, from below; y= 20 – x2 from above.

Q: find the area of the region bounded above by the curve y = 2e^-x + x, below by the curve y = e^x/2,…

A: To find the area of the region bounded above by the curve y=2e-x+x, below by the curve y=ex2 on the…

Q: The area of the region bounded by the two curves y = x²and y 25 is Square Units

A:

Q: Sketch the region enclosed by the given curves and find its area. y = v2x, y = a², 0< x < 6

A: The region is sketch is below:

Q: The area of the region bounded by the curves y = I' and y = 2x is %3D 1/3

A:

Q: Find the area of the region bounded by the three curves y =x², y = 8 – x², and y = 4x + 12.

A:

Q: Find the area of the region bounded by the given curves: y = x² y = 4x – 22

A: Given: y=x2, y=4x-x2 For finding area of region bounded by given curves, we draw graph of both…

Q: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: Find the area of the region bounded by the three curves y = x², x = y³, and x + y = 2.

A: It is given that, y3=x ⇒y=x13let, y=f1(x)=x13y=x2let, y=f2(x)=x2x+y=2⇒y=2-xlet, y=f3(x)=2-x   Area…

Q: The area of the region bounded by the two curves y = x“ and y = 4 is

A:

Q: Find the area of the region enclosed by the curves y = |x² – 4[ and y = 4+

A: We sketch the region using a graphing calculator y=|x2-4| (green)  y=4+ x2/2 (violet)

Q: Calculate the area of the region bounded by the two curves y = x 2 and y = 4 using the formula A = i…

A:

Q: Find the area of the region between the curves y = x² +9 and y interval [-1,3]. = 10 + 2x over the

A: Given that:                      y=x2+9y=10+2xBetween [-1, 3]   NOTE: As per our answering…

Q: The area of the region bounded by the two curves y = r and y = 4 is Square Units

A: Given: y=x2y=4

Q: The area of the region bounded by the curve y = a° – 3x? – x + 3 and y = 0 is

A:

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: Find the area of the region enclosed by the curves x + y: = 0 and x + 2y = 1.

A: Let's find.

Q: Find the area of the region enclosed between the curves defined by the equations y = Vx +2 ,y = x ,…

A: Solve the following

Q: Find the area of the region that is enclosed between the curves y = x² and y = x + 6.

A: The given curves are, y=x2 and y=x+6. The objective is to find the area of the region that is…

Q: Find the area of the region bounded by the given curves.  y=x^2-4x, y=3x+8

A: Let the curves be: The area between curves f(x) and g(x) on an interval [a,b] is given by: Where,…

Q: d the area of the region bounded by the curves y = 3x and y = x².

A: Given query is to find area bounded by the curves.

Q: Find the area of the region enclosed by the line y = 4x and the curve y = x3 + 3x?

A: Given: y=4xy=x3+3x2

Q: Find the area of the region enclosed by the line x = 2y and the curve x = y3 - y?

A: To calculate the area of the region bounded by the curves x=fy and x=gy, use the formula…

Q: Find the area of a region bounded above by the curve y =r' and below by y = 0 over the interval (0,…

A: The region is bounded above by the curve y=x3 and below by the curve y=0. Since the region is over…

Q: The area of the region bounded by the two curves y = x² and y =4 is

A:

Q: a) Find the area of region enclosed by the two curves y = Vx +1 and y= /2x

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: 2 y = x - 3x, y=x 3r.

A:

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

A:

Q: Find the area of the region between the curves y |Jx and y x2-2 | Area between curves

A: Given,

Q: Find the area of the region enclosed by the curves x+y=2y^2 and x+y=2

A:

Q: Find the area of the region R enclosed by the curves y = x3 and y = x3

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Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

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Q: Find the area of the region R enclosed by the curves y = x2 – 2x and the х — ахis.

A: Given: y=x2-2x

Q: Find the area of the region bounded by the curves y – 2x – 1 = 0 and y – x? – 4 = 0.

A:

Q: Find the area of the region bounded by the curves y = 1 (x+1)21 2 y = 4 and

A: Please refer to the image below

Q: Find the area of the region bounded by the two curves. y = x2 + 3 y = 7x + 3

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Q: Find the area of region bounded by the curves x= 2y+6 and x y-1.

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Q: Find the area enclosed by the curve x = t2 - 2t, y = Vt and the y-axis.

A:

Q: Find the area of the region bounded by the given curves. y = 2ax, y = 2ал*, а > 0

A:

Q: The area of the region enclosed by the curves y = x2 - 1 and y = 1 - Ix| is

A:

Q: find  the area of the  region bounded by the  curves y²=4px and x²=4py

A: To find the area.

Q: Find the area of the region enclosed by the given curves  y = 1/4x^2 y = 2x  x+y = 3 while x is…

A: I have done solution step by step in detail...go through the solution

Q: Find the area of the region under the curve y = 6x? + 4x + 3 from x = -1 to x = 2.

A: integration is the process of finding the anti-derivative function of the given function. The…

Q: 3. Find the area of the region between the curves y = Vx and y =x2.

A:

Q: Find the area of the propeller-shaped region enclosed by the curves x - y1/3 = 0 and x - y1/5 = 0.

A: We have the curves x-y13=0 and x-y15=0. We have to find the area of the propeller-shaped region…

Q: Sketch the graph of the given curves and find the area of the region bounded on the left by the…

A: Graph of x=3-2y2, that is gy=3-2y2 is a parabola as function g(y) is in the form of quadratic…

Q: Find the area of the region bounded by the given curve:r = 5e 2 on the interval

A:

Q: Find the area of the region enclosed by the two curves y = 2|x| and y = x² – 3.

A:

Q: Find the area of the region between the curves y=|x| and y=x^2-2

A: Proceed as shown...

Q: Find the area of region enclosed by the two curves y = Vx +1 and y = v2 x

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.