1. Find the area of the regions shaded by the following curves: r = 2cos0 and r 2sine %3|

Q: Question 1 Find the area between the curves y = x and y = 3x + 2.

A: The graph is shown below:

Q: #1 Find the area of the region between y=2x+ and y=x=4

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

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Q: 1. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

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Q: 12. Find the area of the region enclosed between the curves defined by the equations y = √(x + 2), y…

A: We have to evaluate the area of the region bounded by the curve y=x+2 and the line y=x using the…

Q: 1. Find the first quadrant area bounded by the curves 20 y = 4+x2 y = 1 and x = 0

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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: Question (b) Determine the area of the region enclosed by x=y² - 3 and y = x –1.

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Q: 3. Find the first quadrant area bounded by the following curves: y = x² +2, y = 4 and x = 0.

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Q: Question 4 Find the area of the region of the enclosed by the curves y = 39 – x² and y = x² – 33.

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Q: QUESTION 4 Find the area of the region bounded by the given curves. y=x-4x, y = 3x+8 25 a. 3 ОБ. 243…

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Q: Find the area enclosed by the loop of the curve y² = x (x - 1) ². Consider the attached graph.

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Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y

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Q: Q1.A: Find the area of the shaded region shown in figure (1). y = 1 y = x2 x 1+ y2 Figure (1) y = -1

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Q: 1. Find the area of the region between the curves y=x -4 and y=2-x.

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 3) Find the area of the region enclosed by the following line and the curve. y = x – 1 and y² = 4x +…

A: The graph for the given functions y=x-1 and y2=4x+1 is shown below.

Q: (4) Find the area of the region in the first quadrant bounded above by y = √x - 1 and y = x - 3.

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Q: Graph the equations and shade the area of the region between the curves y = x3 and y = x2 − 7x over…

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Q: Question 23 What is the area of the region between y =x-2x-3 and the x-axis from x=0 to x-4?

A: It is required to find the area made by curve between x axis and the given points.

Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

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Q: Question 4. Find the area bounded by the indicated curves. y =x- 9x, y = 0

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Q: Question 17 Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the…

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Q: 20 B-Find the area of the region inside the curve r-1+cose and outside the curve -1 and graph the…

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Q: Question 3: Find the area between the curve y = 6 – x² and the line y = -3x + 2.

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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: (1) Find the area of the region bounded by the curves and draw an illustration y = x² and y = 6x-x².

A: The region bounded by the curves y=x2 and y=6x-x2 Note:    Multiple questions are given we are…

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: Question 5 Find the area of the region enclosed by the curves *=2y3 – 8y2+6y, x=y2-y (A) 12.72 B)…

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Q: 1- Find the area of the region enclosed by the line y=4x and the curve y= x³ + 3x².

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

Q: QUESTION 4 Find the area of the region enclosed by the given curves. y = 15 - x 2, y = x 2-3

A: From the given curve the bounded region is as shown below; Now find the point of intersection…

Q: 1) Sketch the region enclosed by the given curves and find its area. 1 y = x for x > 0 ||

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Q: Find the area of the region enclosed by the given curves. y = 13-x2, y=x2-5

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Q: Question 2 Area bounded by the curves y=e*, y=e", x=0 and x=In2 (А) 604/9 (В) 304/14 C) 502/9 304/7

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Q: Question 4. Compute the Area of the region bounded by the given curves. Y1 = 3x- x2 and Yz = 3 -x

A: Given: y=3x-x2, y=3-x we finding area region bounded by given curve, first we draw graph of both…

Q: Graph the region between the curves. And Compute the area of the region. (Round your answer to five…

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Q: 1. AY -x² +1 y=x

A: we have to find out

Q: Question 8 Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the…

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Q: Find the area of the region between the curves x=((y-2)^2)/3 and y=8-x shown in the following…

A: Explained below

Q: Question 7 Find the area of the region(s) enclosed by the curve f(x) = x³, the x-axis, and the lines…

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Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y ?.

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Q: 3 Given the curve y= x and the line V= 4x in quadrant 1 Find the area of the region bounded by the…

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Q: (b) Find the areas of the regions enclosed by the line Y=* and curve y=x-3x

A: Given: Curves y=x and y=x2-3x Definition: The area between curve f(x)≥g(x) on the interval [a, b] is…

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: )Find the area of the region bounded by the given curves and lines for the following problems:- 1.…

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

Q: Find the area of the region under the given curve from 1 to 2. 13 y = x + 4x

A: As we can calculate the area under the given by integrating the given function for the given…

Q: 18. Find the area of the region enclosed by the curve y = (1- x)²; 0<x< 1. (in QI)

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Q: y=x^3−x^2+x+7​; y=2x^2-x+7

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.