find the volume of the object obtained when one rotates the area under f(x) = cosx²)and over 0

Q: Consider the region R enclosed by y = sin 2x , y = cos x over the interval [π/6, 5π/6] on the x…

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Q: Find the area under the curve f(x) = 2x* from x = - 3 to x = 2. Area %3D

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Q: Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 5…

A: The volume of the solid generated by a region under f(x) bounded by the x-axis and vertical lines x…

Q: Find the area bounded by the curve x = (y+1)2 and y+1 = x2. Show complete solution of points of…

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Q: The region is bounded by x+6=0 and y^2+x+2=0 is revolved about x=-6. find the integral in finding…

A: Consider the provided question, The volume for solid of revolution between the curves x+6=0 and…

Q: Find the area between the curve y = -x< + 6x – 8 and the x-axis from x = 2 to x = 4. (Give an exact…

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Q: Write a definite integral for the area of the region bounded by y = 2 - x² and y = x2. Do not…

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Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum.

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Q: Find the area A of the region that is bounded between the curve f(x) = -4 sin () and the curve g(x)…

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Q: Each integral represents the volume of a solid.Describe the solid.   ∫0π/42 π (π - x) (Cos x - Sinx)…

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Q: ) Find the area bounded by Y,=cos(x) Y,= sin(x) X-0 and X-IT/2 graph it and show

A: Find the point of intersection of 2 curves.

Q: nich integral represents the length of the graph of y = In(1 – x²) over the interval [0, ]:

A: here option A is true because length is given by =1+(dydx)2dx so here…

Q: use the limit of the Riemann Sum to find exacct area under the curve. fCx) = 4 x [2,5]

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Q: The region R is bounded by the parabola y = x2 and the line y = 1. Set up definite integrals to find…

A: The equation of parabola is y=x2 and the line is y=1.

Q: Find the area between the furve f(x) =sinx and g(x) = cosx over the interval [90. 360] y=4x+16 x=--2…

A: Dear as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Find the area under 3 sin(x) and above y = 3 cos(x) for 0 < x < T. that this area may not be defined…

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Q: Sketch the region enclosed by the curves and find its area. y = cos 8x, y = 0, x = x = 16' 8 NOTE:…

A: The region enclosed by the curves y=cos8x, y=0, x=π16, x=π8

Q: Find the area enclosed by the curves below from x = 0 to x = 3 y = 33 cos(3x) y = 33 sin(3x) Area =

A: Given:- y=33 sin(3x) , y=33 cos(3x)  To find:- Area enclosed by curves from x=0 to x=π/3

Q: FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS,…

A: Given region is bounded by the graph of  y=9-x2, The X-axis and Y-axis

Q: Find the area of the surface formed by revolving y = x³ on 0 < x<1 around the x-axis. Show all steps…

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Q: Find the of region bounded by the functions f(x) : (В) sin x and g(x) = cos x over the interval [0,…

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Q: The area of the region bounded by the graphs of y = x3 and y = x cannot be found by the single…

A: Given: y=x3, y=x for finding area of region bounded by given curves, first we draw graph of each…

Q: Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to…

A: Given query is to find the value of the integral

Q: 2. Find the volume of a cylinder with a radius of r and height h by integration.

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Q: Sketch the graph. Set up (DO Not Evaluate) an integral for the volume of the solid that results when…

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Q: Find the area under the curve 3 over the interval [3, 8]. y = (4x + 2)² Enter the exact answer. area…

A: y = 34x+22,interval : 3, 8

Q: 5. Find the volume of the solid formed when the area in the first quadrant bounded by the graph of y…

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Q: Find the area bounded by the curves y=sin x and y= cos x from x =0 tox= 7. Make a sketch and shade…

A: The region bounded by the curves y=sinx and y=cosx from x=0 to x=π

Q: A Bundt cake, well known for having a ringed shape, is formedby revolving around the y-axis the…

A: Given:              When the ring shaped cake is revolved about y-axis, Then:                   To…

Q: Estimate the area under the graph of f(x) = 2x + 16x + 35 over the interval (0, 4] using ten…

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Q: Find the definite integral that will compute for the area of the region bounded by y = tan x, x = 0…

A: We can find the area bounded by the curve .

Q: Find the area of the region enclosed between f(x) = 0.2x + 6, g(x) = x, x = -2, and > Area =

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Q: Find the volume generated by revolving about the line x=0 the area under the arch of the sine curvey…

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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: find the area of the region bounded by y = x+2 and y=x^2.Use double integral to solve the question.

A: Solution-

Q: Show that Gabriel's horn, a volume of revolution from one to infinity of f(x)=1/x, has an infinite…

A: We have to show that Gabriel's horn, a volume of revolution from 1 to ∞ of f(x)=1/x, has an infinite…

Q: y = sin(x), y = 2x

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Q: Sketch the region enclosed by the curves and find its area. y = cos 5x, y = 0, x 10' NOTE: Enter the…

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Q: Estimate the area under the curve from x=0 to x=5 using 5 approximating rectangles and left endpoir…

A: In this question, the concept of Riemann Sum is applied. Riemann Sum To estimate ∫abfxdx, Riemann…

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

A: To find the area:

Q: Solve using iterated integrals. (with graph) Find the smaller area cut from the circle x2 +y2 = 25…

A: The objective is to find the smaller area cut from the circle x2 +y2 = 25 and x=3.

Q: Evaluate the double integral that will solve for the area of the region bounded 2. by y = cos (x) +…

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Q: Find the area between y = 16 sin (x) and y = 16 cos (x) over the interval [0, n]. (Use decimal…

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Q: A solid is generated by revolving about the x-axis the region in the first quadrant bounded by the…

A: It is given that, y=1+sin2x,x=π2   Volume of solid formed by revolving the first quadrant region…

Q: Find the approximation of the area under the curve using 4 trapezoids. Use the function y = x2 - 4x…

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Q: Find the area of the region bounded by the graph of f(x) = x sin x and the x-axis between x = 0 and…

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Q: Solids of Revolution ( refer to the image )

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Q: Approximate the area under the curve f(x)=sin2(πx) using the midpoint approximation rule with 3…

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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.