1. Find the area of the region bounded by the curve y = f (x) = |a² – 4| and the lines x = -3, and x = 1.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: 1.) Find the area bounded by the region x = 4y + 4 and y= x+ 2

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Q: Find the area bounded by the following: 1. Curve y²-8y-8x +32= 0 and y²-8y + 4x = 0

A: We will use basic knowledge of integral calculus and the theory of evaluation of integrals.

Q: 1. (a.) Find the area bounded by the two curves; y=r+x-10 and y=-+Sx+6. i y=r-3r and y = 2-x

A: i) Given curves are, y=x2+x-10 & y=-x2+5x+6 Let's draw table for y=x2+x-10 x 0 1 2 4 y -10…

Q: Find the area between the curve of X = 5 4 3 2 1 1 2 3 O 2.749 O 3.296 4.159 4.957 4 5 33 and the…

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Q: Q4. Find the area between curve y = x - 3x + 2 and x-axis from x =0 to x 2

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Q: 1200 1100 1000 900 800 700 600 500 400 300 200 100 100 Find the (exact) area under the curve y = 4x*…

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Q: Find the area of the region between the curve and the x-axis. In 4 3x f(x) = e - 4 from 0 to 3

A: By using area formula, we calculate the required area of the region.

Q: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3

A: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: 1+x² 1. Find the area of the region bounded by the curve y=- and the lines y = 0, y = x, x = 2. 2x2

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Q: 9. (a) Calculate the area of the region bounded by the curves y = x² +1 and y = xª between x = 0 and…

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Q: 9. What is the area of the region between the graphs of y=x2and y =-x from %3D x=0 to x= 1. A) 1 B)…

A: Topic = Area

Q: 1. Find the area of the region bounded above by the curve y = 2e-* + x, below by the curve y = , on…

A: We have to find out the area of the region bounded above by the curve   y = 2e-x + x , below by the…

Q: 4- Find the area of the region bounded by the curves y - 3x = 4 and 3r – 2y = 11. a) b) e) d) e)

A: The equation of the curves are : C1 :  y2-3x = 4  ⇒ x = y2-43 C2 : 3x-2y = 11  ⇒ x = 2y+113 To…

Q: 1. Sketch the region R between the functions y = 2x and y = x2

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

Q: 3. Find the area bounded by the curve ay² = r8 and the line * = 4 a. Ans. 142 a².

A: Find the area bounded by the curve.

Q: - 7. Find the area bounded by the curve y² + x − 4y = 5 and the y — axis

A: We have to find the area of the given curve and line.

Q: 1. Find the area bounded between the curves: y = x°, x = 1, and y -8

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Q: 1. Find the area under the curve y a. f(x) = x³ [2,3] b. f(x) = 3√x [1,4] (x) over the stated…

A: a) fx=x3          2,3 b) fx=3x          1,4 Find the area under the curve y=fx over the stated…

Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

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Q: In(6z) – 1 Find the area of the region lying between the x-axis and the curve y = to the right of…

A: The area of the region lying between the x-axis and the curve yx=ln6x-1x2 to the right of the line…

Q: If L2 is the sum of the approximating rectangles for the area under the curve y = | cos x| from 2n…

A: Solve the following using left end points approximation

Q: Suppose that 0 <c <n/2. For what value of c is the area of the region enclosed by the curves y=cosx,…

A: Suppose that 0 &lt; c &lt; π2. We have to find the value of c at which the area of the region…

Q: Find the area under the curve between x-2 and x=-1 for the curve f(x)=(7 – x²)d

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Q: In(5z) – 1 to Find the area of the region lying between the r-axis and the curve y the right of the…

A: Using integration by parts,

Q: 7. Find the area bounded by the curve y = x² + x + 4, the x-axis and the ordinates x = 1 and x = 3.

A: The area under the curve y=f(x) in the interval a, b is calculated using the formula: A=∫aby dx. We…

Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

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Q: 1. Find the area bounded by y2 = 4a(y – x), y² = 2a(x + 2y – 3a) and the x-axis.

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Q: 1. Find the area bounded by the curve y = x^2, the x- axis, and the ordinates x = 1 and x = 3.

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Q: 1)Find the area bounded by the given curves. a)y = 3x2 − 12 and y = 0 b)y = x2 − 2 and y = 10 −…

A: we have been given the function y=3x2-12 and y=0 and the formula of the area under the curve is…

Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

Q: 6. Find the area bounded by: d. The curves y=x-4, y38-2x.

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Q: 2 3. Find the area of the unbounded region between the x-axis and y=- for x26. (x-4)

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Q: Find the area of the region enclosed by the curves f(x) = 7x + 1 and g(x) = 5x + 17, and the lines x…

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Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

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Q: Let f(x) 4x³ and g(x) = sin (Tx) and R is the region bounded by the two %3D functions on the…

A: The slope of a tangent to a curve at a point is obtained by calculating the derivative of the curve…

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: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

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Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

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

Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: 1/ Find the area of the region enclosed between the curves y= 2r'+10 and y=4x+16 and x=-2 and x=5?…

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Q: Find the area between the curve f(x) = −3x^2 + 3 and the x-axis over the interval [−1, 2].

A: Answer and explanation is given below

Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: 19. (a) Find the area bounded by the curves y = 2x2 and y = 4x. (b) Two cars both start on a journey…

A: Given two functions: y=2x2 and y=4x To find a) Area under the two curves b) If two curves represent…

Q: Find the area of the region bounded by the curve y = x³ – 2x² – x + 2 and the x-axis for -1 <x<2, as…

A: We will solve this question by using double integration. where,  y=0 and y=x3-2x2-x+2 and x lies…

Q: 17) Find the area bounded by the curve 4x - 3y + 19 =0, y-axis, the lines y = 1 and y = 5.* O a) 15…

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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.