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

Q: Find the area under the curve y=3x2+x+2e*/2 from x=0 to x=1.

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Q: 7) Find the area under the parabola y = x² – 2x +2, above the x-axis and between x = 0 and x = 1.

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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. Find the area of the region bounded by the parabola x = 3 + 2y – y? and the line 2x + 3y = 6.

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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: Find the area between the curve and the x-axis for the function y = x2 +3x between x= -1 and x = 2…

A: To

Q: Find the area of the region bounded between the curves y = sin(x), y = cos(x) on the following 4 -27…

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Q: šin(3x) Find the area bounded by the curve y = ,0 <x<T/3 and the line y = 0 as shown 2+cos(3x) in…

A: Given y=sin3x2+cos3x, 0≤x≤π3 and the line y=0

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 bounded by the given curve: 16x² +9y² − 64x + 18y-71 = 0 and x² + y² − 4x − 4y+4=0

A: Given the curves, C1:16x2+9y2-64x+18y-71=0C2:x2+y2-4x-4y+4=0. Rewriting, we get…

Q: Find the area of the region bounded by the graph of f(x) = 4 − x2, the x-axis, and the vertical…

A: Given curves: The graph is:

Q: In(7x) – 1 Find the area of the region lying between the a-axis and the curve y = to the right of…

A: We have to find the expression of the area of required problem.

Q: Find the area under the curve y = 3x 2 from = 1 to x = 2 .

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

Q: Find the area under the curve from x = 0 to x = 1 of y = (x 4 + x)5 (4x 3 + 1).

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Q: . Find a number k > 0 such that the area of the region bounded by the curves y = x², and y =k – x2…

A: As per as our guide line I am supposed to answer only one question from these 2 question Please…

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: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

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Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: 1. Determine the area bounded by curves y = -x² + 4x + 3 and y = −x³ + 7x² − 10x + 5 over the…

A: We have to find the area bounded by the curves.

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 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: (In x) – 1 Find the area bounded by the curve y= and its asymptotes. A = ∞

A: Find the area bounded by the curve y=ln x-1xA=∞ and its asymptotes Given curve, fx=y=ln x-1x→ay…

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

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Q: 1) Determine the area of the largest possible rectangle whose base is on the x-axis and the top two…

A: Given the rectangle whose base is lies on x axis and the top two corners lie on the curve y=9-x2

Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x 6 Sketch the region bounded by the…

A: Solved below

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: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: Find the area of the region bounded to the right by x = y + 2 and to the left by x = y². 543-2 1…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

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 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: 7. Find the area of the region under the curve y= |2x – 1| between x= O and x= 2.

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Q: Find the area under the curve y = - - over the interval [4, 9]. (4x + 2)² Enter the exact answer.…

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

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Q: Find the area of the region lying to the right of x = y2 - 5 and to theleft of x = 3 - y2.

A: Given: f(y)=y2-5 and g(y)=3-y2 To find: Where the curve intersect and it is calculated when…

Q: 4/2 x2 -1 for [0, 1]. Find the length of the curve y=- Find the area of the curve bounded by the…

A: (7)We will find the length of the curve.

Q: Find the area of the region lying between the x-axis and the curve In(82) – 1 to the right of the…

A: Given curve is: y=ln8x-1x2 The area of region of the curve lying between x-axis and right of the…

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: Calculate the surface area of revolution of f(x) = 3√(x) + 2 about the y-axis in [2,8]. Graph.

A: Given data:   The expression for the given function is: f(x)=x1/3+2.   The expression for the given…

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: The area between z = −2.27 and z = 1.41 is .

A: P(-2.27&lt;z&lt;1.41)=?

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: Find the area under the curve of y=-+x+5 from x=-1 to x -4 with n-5 right endpoint rectangles. O 18…

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

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Q: The area under the curve y = 7x bounded by the lines x = 4 and x = 8 above the x – axis is O 336.00…

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Q: Find the area of the region bounded by the curvesr = 2 cos 30 and x = y – 1.

A: The curves given are as follows: r=2cos3θx=y2-1 We know that x=rcos3θ, y=rsin3θ.…

Q: 7- The area of the (bounded) region between the line y = x quadrant is and the curve y = x² in the…

A: 7) The area of the region between the line y=x and y=x2 in the first quadrant. First we draw the…

Q: 1. Find the area of the region bounded by y = x² - 3 and y = 5 - x².

A: This question can be solved using the concept of area bounded by two curves.

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…

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.