Find the area bounded by the curve x = sin 2y - cos 2y , the lines y = and y = T ano the y-axis.

Q: Find the area of the region that lies under the curve, y = sin x on the interval 0< x <;

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Q: Find the volumMe generated by revolving the area bounded by the giveN Curve and avd lines y = x', x…

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Q: Find the area bounded by the curves an arch of y= (4)sin (xA)

A: Given:        y=14sinx4 The area under the curve is the area between a curve f(x) and x-axis on the…

Q: Find the area of the region bounded by the given curves. y = sin2(x),    y = sin3(x),    0 ≤ x ≤ π

A: Given: Find the area of the region bounded by the given curves. y = sin2(x), y = sin3(x),    0 ≤ x ≤…

Q: Find the area of the region by bounded by y = 4x and y = 2x – 4 by integrating with respect to y.…

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Q: Find the area bounded by the curve x y2 +2y and the line z = 3. %3D

A: Given :                curve x = y2 + 2y and the line is x = 3 To find :               The area…

Q: Find the area enclosed by the curve y=(x)^1/2, the tangent to the curve at x=4 and y axis.

A: Consider the provided information, y=x12 The tangent to the curve at x=4 and y axis. Find the area…

Q: Find the moment of inertia of the area bounded by the curve x^2 = 8y, the line x = 4 and the x-axis…

A: Given curves are x2=8y, x=4 and the x−axis. We have to find the moment of inertia of the area…

Q: The area bounded by the curve x = 5y + 8, the y-axis and the abscissas y = 0 and %3D y = 2 is

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Q: Find the area of the region bounded by the two curves x = sin2y and x = cos2y from y to y = n 8

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Q: Compute the surface area of revolution of y=sinxy=sin⁡x about the x-axis over the interval [0,7π]

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Q: Find the area of the region bounded by the given curves. y = sin2(x), y = sin3(x), 0 < x < A

A: The area between two curves f(x) and g(x) on an interval [a,b] is given by Given,

Q: Find the line y=mx that divides the area under the curve y=x(1-x) over [0,1] into two regions of…

A: Given,           The line y = mx that divides the area under the curve y = x(1-x) over [0,1] into…

Q: Determine the moment of inertia of the area bound by the two curves about the x and y axis. y y = x?…

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Q: Find the area of the region bounded by the curves 3 y = sin(x), y = sin°(x), x = T/2. 0, and x =

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Q: Find the area bounded by the curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: Find the line y = mx that divides the area under the curve y = x(1 − x) over [0, 1] into two regions…

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Q: Find the area in the first quadrant bounded by y=3x, y=0 and y=4 by integrating with respect to y.

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Q: Find the area of the region bounded by the curves: y=cosx, y=sin2x, x=0, x=pi/2

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Q: Find the area of the region bounded by the curves: y= cos x, y=sin4x, x=0, x=pi/2

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Q: Find the surface area of revolution about the x-axis of y = 3 sin(6x) over the interval 0 <x < -

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Q: Find the area of the region which is bounded by y = sin x - 3, y = 3x, y-axis and x = 2. Leave your…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the moment of inertia of the area bounded by the curve x2=4y, the line y=1 and the y-axis on…

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Q: Find the area between the curve y = sin x and the line segment joining the points (0, 0) and (5π/6,…

A: Consider: y=sin x and line joining the points 0,0 and 5π6,12. Find the area between them.   First…

Q: Find the area of the region enclosed by the curves y = 4 sin x and y = 4 sin 2x for 0sxST. y = 4 sin…

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Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 3. Leave your…

A: Area bounded by the given curves :If f(x) and g(x) be two continuous function on a,b and f(x) ≥g(x)…

Q: Find the area of the region bounded by y = cos x, y = sin x, x = 0, x =

A: Please see the diagram below:

Q: Find the area bounded by the curve x = cos(t), y = e', 0sts and the lines y = 1 and x = 0. 2

A: The solution are next step

Q: Find the moment of inertia with respect to y-axis the area bounded by a²y = x³ , the x-axis, and the…

A: Given....

Q: Find the area bounded by the curve y=x³, x=0, y=1 is revolved about the x axis.

A: The graph of the curves is

Q: Find the area of the region enclosed by the curves y=x^2 and y=6x by integrating with respect to y.…

A: Follow the procedure given below.

Q: Find the area bounded between two points of intersection of y = 3 sin and y = 3 cos

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Q: Find the area of the region by bounded by y = 4x and y = 2x – 4 by integrating with respect to y.…

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Q: Find the area of the region bounded by the x-axis and the curves y = 2 sin(x) and y = 2 cos(x) where…

A: First draw the graph of the both function and define the required area to be calculated.

Q: Find the area of the region enclosed by the curves y = 7sin x and y=sin (7x), 0≤x≤t.

A: The region enclosed by the curve y=7 sinx and y=sin(7x), 0≤x≤π

Q: Find the area bounded by the curves y = sin x +1 and y = 3 – sin x on the interval E, %3D

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Q: Find the area between the curves y = |x| y = cos(x)

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Q: Find the moment of inertia of the area bounded by the given curves with respect to the specified…

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = =9y-y2 and y = 2

A: Follow the steps.

Q: Find the moment of inertia of the area bounded by the curve y^2 = 4x, the line y = 4, the y-axis on…

A: Moment of Inertia about x-axis

Q: Find the area of R - region bounded by the curve y = 1/x2 and the lines y = x and y = x/8 O 1

A: Given: The curve y = 1x2 and the lines y = x and y = x8. To find: The area of the region bounded by…

Q: Find the moment of inertia with respect to the y-axis of the area bounded by the curve y=1-x3 and…

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Q: Find the area bounded by the curve x = y^2 + 2y and the line x = 3

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Q: Find the surface area of revolution about the x-axis of y = 4 sin(4x) over the interval 0 < x < 4

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Q: Find the area of the shaded region bounded by the two axes and the curve y = 2 sin(x) + 1. F(x) E 2…

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Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

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Q: a) Find the area between the two curves y = 6 – x and y = x² by (i) integrating with respect to x…

A: Given curves: y=6-x and y=x2 To find: The area between the two curves y=6-x and y=x2 by…

Q: Find the area between the curve y = cos (2x) and the line joining the points (,0) and (등, 글).

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: Find the moment of inertia with respect to x-axis the area bounded by 2y2 - 8y - 16x + 16 = 0 and…

A: The solution are next step

Q: Find the area of the region between the curves y = sin(nx/2) and y = x. Area between curves =

A: In the question it is asked to calculate the area between two curves y=sin(πx2). and y=x.

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.