Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by integrating a function with respect to x then by integrating with respect to y.

Q: /Find the area under the curve y = sin x cos 2x from x=0 to x =-

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Evaluate the integral using tabular integration by parts. 4 x° V2 x + 1 dx +C

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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 area of the region that is bounded by two curves y = sin x and y = cos x from x = 0 to x =…

A: Here, to find the area bounded by the curves y=sin x  and y=cos x from x=0 to x=π2. The region is as…

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: x = y² and the line y = x − 2

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Q: Sketch the region bounded by the curves y = vx + 4 , y=x +2 and evaluate the area.

A: Given Curves are     y = x+4   and    y = x+2  first equation can also be written as  x = y2 -4 now…

Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

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Q: calculate the area between y=x^3 and its tangent at the point (1,1)

A: The slope of the tangent is given by y' at (x,y)=(1,1) y'=3x2At x=1y'=3 Equation of tangent line is…

Q: Find the region bounded by the curves y = x and y = x² using a dx integral.

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Q: Make a sketch to show a case in which the area bounded by two curves is most easily found by…

A: To graph: The sketch to show a case in which the area bounded by the two curves is most easily found…

Q: Find the area between the given curves: f(x) = sinx g(x) = cosx on the interval (0, π)

A: Sketch the region bounded by the curves fx=sinx  and  gx=cosx   on 0, π as shown below.

Q: Find the area bounded by the curve y = x 2 and y = 2 − x 2

A: To find area bounded by the curves y=x2 and y=2-x2.

Q: Sketch the region between y = sin x and y = cos x over the interval and find its area: [0, π]

A: Consider the given function as y=sinx and y=cosx

Q: Use a single variable integral to find the area bounded by the curves x = 0, y = 24, and y = e.

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Q: Find the area bounded by the curves y= x', x = 2, and y = 0 using double integration.

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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 area under the curve y = 5xe-* for x > 0. %3D area %3D

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Q: I. Find the area bounded by the curves y=x', y 1, and x = 0 using double integration.

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Q: find the area of a region bounded by the curves y= x^3, y= x ln(x^2), x=1 and x=2

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Q: Find the area of the region under the given curve from 1 to 6. x2 + 6 y = 7x — х2

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Q: Use an iterated integral to find the area of the region. y = 4-x2 dy dx = WebAssign Plot 1 -1-

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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: Sketch the region whose area is given by the definite integral. 8. x dx

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Q: Find the area bounded by the curves y= sin 2x and y=cos 2x in 0,

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Q: Find the area bounded by the curves y = x³, y = 1, and x = 0 using double integration.

A: Area of the required region is 3/4 see below the calculation

Q: Compute the area of the region which lies to the right of the parabola x = y^2 – 12 and to the left…

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Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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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 area bounded by the ,3 curves y = x°, y= 1, and x using double integration.

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Q: Sketch the region enclosed by the curves y = (x-2)2 and y=x then find its area using the…

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Q: Find the area of the region between the curve y = 3 - x2 and the line y = -1 by integrating with…

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Q: Find the area bounded by the curve y = e^x , y = e^-x and x = 1, by integration.

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Q: Sketch the region bounded above by the curve (9e^−x)*sin(πx), the x-axis, and x = 1, and find the…

A: We have to sketch the region bounded by the curve 9e-xsinπx, x-axis, and x=1, and also find the area…

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: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine its area…

A: Sketch the bounded region.

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: Sketch the region enclosed by the curves: y= x^2-1, y = 7-x^2. Then set up (but do not evaluate) the…

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Q: What is the area under the curve y = cosx over the interval [0 ,π/2]?

A: Integrating the equation of curve in the given interval gives the area

Q: Find the area of the region bounded by the given curves. Decide whether to integrate with respect to…

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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: Sketch the region enclosed by the curves and find its area. y=e^x, y=e^3x, x=0, x=ln 3

A: The area between the y=f(x)  and  y=g(x)  on the interval [a,b] is given by,∫abf(x)-g(x)dxWhere,…

Q: x = y² - 2y and x = 4y - y²

A: The given curves are; x=y2-2y and x=4y-y2 Now find the point of intersection between the given…

Q: Sketch the region enclosed by the curves 4x+y2=12 and y=x then find its area using the appropriate…

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Q: Sketch the region enclosed by the curves y=2 and y =-2x+3 then find its area using the appropriate…

A: Consider the following curves: y=-2x+3y=2 Intersection point of curves: -2x+3=2-2x=-1x=12…

Q: make a sketch to show a case in which the area bounded by two curves is most eassily found by…

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Q: Find the area bounded by the curves y = x3 , y = 1, and x = 0 using double integration.

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Q: y=x, 4x +y“ = 12

A: The region is bounded by the curves,    y=x, 4x+y2=12

Q: 4) Sketch the region and find the area bounded by + = 1, y = ±3 and y = x + 4 using double…

A: We have to find the area of the region.

Q: . Calculate the area bounded by the curve y= 4(x – 1) and the x -axis. A)

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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.