Find the area between the curve y = cos (2x) and the line joining the points (pi/4, 0) and (pi/6, 1/2)

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: 6.4.12 Please help me solve these math practice questions.

A: Area of the curve y= cos(4x)  Where -π/8<x<π/8

Q: Evaluate the integral. (Use C for the constant of integration.) 6 arctan(Vx) dx

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Q: Express the length of the curve as an integral but do not evaluate it. r = sin θ cos θ, 0 ≤ θ ≤ π

A: We have givem expression r=sinθcosθ, 0≤θ≤π We have to set up the integral for calculate the length…

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: Sketch the region that lies between the curves y = 4 sin(x) and y = 3 cos(x) from x = 0 to x = 0.37.…

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Q: What is the area under the curve f(x) = sinx over the interval [0, pi/2]

A: First:                  Let's draw the graph of the curve f(x)=sin x  over the interval: [0, π2]…

Q: Find the area of the region between the curves y = sin(x), y = sin(2x), x = 0, and x = t/2. Area…

A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: Evaluate the integral ſ sin x dx by the method of geometry.

A:

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 of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: Find the area enclosed by the curve whose equation is given below: r = 1- 0.6 sin 0

A: Given curve is r=1−0.6sinθ We have to find the area enclosed by the curve r=1−0.6sinθ Area is given…

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 each piece of the graph after sectioning off between x values. The Definite…

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Q: Find the area under one arch of the cycloid x = a(t-sint) , y = a(1-cost)

A: Introduction: A cycloid is a two-dimensional curve that is constructed with half circles. One arc of…

Q: sin(z)

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Q: Set up integrals To find the area of the regions between the curve of y=4 cos x and the x axis for 0…

A: The Solution is given below

Q: Evaluate the integral. (Use C for the constant of integration.) 9x cos(8x) dx

A: Integrate this by integration by parts

Q: ) Find the area of the surface that is obtained by rotating the curve Y = 0.25X² – 0.5 Log.X, 1<X<2…

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Q: determine the area of the curve r = v V3 cos e + sin 0 that is below the r-axis.

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Q: Find the area of each piece of the graph after sectioning off between x values. The Definite…

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Q: Find the area under curve y= (e*/x )dx from x=0 to x-4. use midpoint method with n=D4

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Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A: The solution are next step

Q: The area under the curve y = cos x from x = a to x = is 0.2. What is the value of a 2 rounded to…

A: Area under a curve y(x) is given by ∫abydx         where a≤x≤b

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 y = sin²(x) and y = sin5(x) from 0 < x<

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Q: Find the area under y = 2 sin(x) + 2 cos(x) and above the x-axis from x = 0 to x = Tt/2. Leave your…

A: The given function is,

Q: Evaluate the integral. (Use C for the constant of integration.) x cos(6x) dx

A: Let, u=x and dv=cos(6x)

Q: Find the area under the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

Q: Find the trigonometric integral. (Use C for the constant of integration.) sin(x) cos os°(x) dx

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Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

A:

Q: 1. Find the area of the region bounded by the curves y=sin X16 , y = 0, and x = 6 obtained by…

A: topic - Area bounded by curves

Q: Set up an integral that represents the arc length of the curve y 2xi from the point (0, 0) to (2,…

A: our objective is to setup the arc length formula

Q: Find the area under the graph of y=sin3xcos2x integrate from 0 to pi/4

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Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

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Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

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Q: evaluate using Integration by Parts.

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Q: Use double integrals to find the area inside the curve  r = 3 + sin(θ).

A: Find the area enclosed by the curve r = 3+sin θ , using double integration method.

Q: find Sexcos'x dx by using integral by Parts.

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

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Q: Approximate the integral to three decimal places using the indicated rule. 9 cos(x) r0.9 dx;…

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Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: Find the area of the segment cut off from the curve y = sinx, 0≤x≤nt by the line y = 1/√2. HT 1/2 y…

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Q: Evaluate the integral. (Use C for the constant of integration.) 5x cos(4x) dx

A: Given, ∫5xcos4xdx We have to evaluate the integral.

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A:

Q: Find the area under the curve y = sin 2t from t = 0 to t = π/4.

A: We have to find the area under the curve of a function y=sin2t , here we have the limit from 0 to…

Q: b. Find by double integration the area enclosed by the curve r= a(1+ cos 0) between 0 = 0 and 0=T.…

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Q: Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by…

A: To graph the function, solve the given equation for y. Since the region is in the first quadrant,…

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: Consider the given integral as  2π∫-5581-x2dx

Q: find the indefinity integral  x^9 dx

A:

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.