Sketch the graph of y = 2x on the interval [0, 3]. Shade the area between the curve and the x-axis. Find the shaded area using basic gemetry.

Q: Find the area of a region bounded by the curves y=e^(2x) - x^3 , the y-axis and x=1

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Q: B- Find the area between the curves: x = y2 and y = x - 2

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Q: Find the area between the curves. y = x2 and y = - x2+18.

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Q: Find the area enclosed by the x axis and the curve y= 4-x2

A: Find the area enclosed by the x axis and the curve y= 4-x2

Q: Find the area between the curves x = y-1 and x =

A: Given:- x=y2 -1, x =2y2 -2 To find:- Area between given curves

Q: Find the area of the region under the curve y 3x +2x, the x-axis, x=0 and x 4. 0

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Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: . Find the area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

Q: Sketch the curve and find the total area between the curve and the Given interval on the x axis…

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Q: Find the area of the curve y = x° – 2x – 3 between x =- 1 to x = 3.

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Q: Find the area between the CUoyes y=9-x² and y= -5

A: For any two curves f(x) and g(x) which intersect at points with x-coordinates a and b and bound a…

Q: Find the area between the curves y = x2− 6 and y = x/2 − 3. Convert a and b to decimals

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Q: I- Find the area of the region bounded from the right by the curve x 4-y, from the left by the line…

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Q: Find the area between the curve y (2.x + 3)2 and the x-axis, from x = -2 to x = 3.

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Q: Find the area between the curves.

A: Given: The curves are y =x and y =xx  .

Q: Find the area in the first quadrant that lies within the curve r 1+ cose.

A: Here,  r = 1+ cos(theta) We know that,  Area = 1/2  {integral of r2 w.r.t theta}

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area enclosed by the given curves. 11) Find the area between the curve y = 6x/(1 + x2) and…

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Q: Calculate the area enclosed by the f(x) = x3 – 6x² + 8x and the x-axis. curve

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Q: Find the area of the region between the curves (x = y² ) and (x = y + 2 ) in the first quadrant.

A: The formula to find the area under the region between the curves is Area=∫y=ay=b[f1(y)-f2(y)]dy.…

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

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Q: Find the area between the curve y = x – and y = -x + 10x2 – 24x 10x + 24x

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Q: Find the area enclosed by the x-axis and the curve y = -x² + 9.

A: Given, We have to find the area enclosed by the x-axis and the curve y=-x2+9.

Q: Find the area between x-axis and the curve defined by   y=2·x2−6·x on the interval [0‍,4].

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Q: Find the area of the region in the first quadrant bounded by the line y = x, the line x = 2, the…

A: the area of the region in the first quadrant bounded by the line y = x, the line x = 2, the curve y…

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis. Answer:

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Q: Find the area under the curve of the parabola y = x? - 2x + 2, above the x-axis and between x=0 and…

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Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

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Q: Find the area between the following curves: x = y +1 and x = y² – 1

A: topic - area bounded by curves

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

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Q: Find the area between the curves y = x² + 1 and y = x + 1.

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Q: Q/ A/ Find the area between the curve y 3x- x² and the x-axis

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Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

Q: Find area of the region under the curve y = 5x - 4 and above the x-axis, for 3 < x < 5.

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Q: Find the area of the region between the curve y = 21-x and the interval -1≤ x ≤ 1 of the x-axis.

A: Given: y=21-x, -1,1

Q: find the area between the curves y=Vx and y x for

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Q: Sketch and find the area of the region below the interval [-6,-5] and above the curve y 器.

A: Given, Find area above y=x325 and below [-6,5]

Q: Sketch the graph and find the area bounded by the curves for y = 2x² and y = x² + 4

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

Q: Find the area contained by the curve y x(x – 1)(x + 1) and the x – axis.

A: Graph of the function y=x(x-1)(x+1) will be as following

Q: (b) / Find the area of the region between the curve y = 3 – x? and the line y = -1.

A: Area between two curves Let  f(x)  and  g(x)  be continuous functions such that  f(x)≥g(x)  over an…

Q: The area enclosed between the x-axis and the curve y=x2 between x=1 and x=2 is:

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Q: Is it possible to get the area between y2 = 3x and y = x3, using  a. vertical strips b. horizontal…

A: Given  The equations are y2=3x  and  y=x3 .     Formula :- Area under the curve  a) vertical strip…

Q: Find the area between the curve and the x axis over the indicated interval. Y=4-x square; [-2,2|

A: Given: Y=4-x2 to find out: area between the curve and the x -axis over the interval [-2,2]

Q: Use a graphing utility to locate the points of intersection of y = e −x and y = 1 − x2 and find the…

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Q: Sketch the region bounded by the curve 3xe¯", the x-axis, and x = 4, and find the area of the…

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Q: Sketch the region below the curve y = x – x² and above the x-axis and find its area.

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Q: Approximate the area between the curve J(x)=-x²+18x and the X axis on the interval 0, 18 |using 6,…

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Q: Find the area between the curves y = e0.3se y = 1.9x + 1 from x = 0 to x and = 5. Area =

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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.