Find the area shared between the curves r = cos(θ) and r^2 = 3 cos(2θ)/2

Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

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Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

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

A: Given,

Q: Use Integration by parts or tabular integration to evaluate (x² + 3x + 6)(sin(2x)) · dx

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Q: Evaluate using techniques of integration or integration by parts

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Q: Use integration tables to find or evaluate the integral.

A: The question is taken from the calculus in which we have to find the integral of given question We…

Q: sinxcos 2x dx

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Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

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Q: Evaluate |x* cos.xdx by using integration by parts or tabular integration.

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Q: Use the midpoint rule with four subdivisions to estimate ∫2 to 6 (2x2+3)dx to two decimal places.…

A: Given ∫262x2+3dx we have to use midpoint rule

Q: Estimate (2x – 5) dx using right endpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: We have to estimate the , ∫15(2x-5)dx using right end points for n=3

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: The area between y= 2sinx and y = sin2x for 0<x ST is

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Q: area bounded by the curve and perimeter when r^2=sin theta +cos theta

A: We used Octave to plot the above curve. And the code is:  theta=linspace(0,2*pi,1000);…

Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

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Q: Choose the integral that would find the area inside r = 3 sin 0 and outside r = 2- sin 0

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Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

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Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: The given integral is,

Q: 3. Using left and right endpoints give two area approximations for f(x) = sin(x) using four…

A: Lets calculate this on interval x = 0 to x = π  divide this interval in four rectangles,  so,  h =…

Q: Explain the application of integration to area.

A: .

Q: x = -sin 2y x = cos y --

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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 intersection area between r = 3sine and T = 2 - sine curves.

A: given, r=3sinθ  and r=2-sinθ

Q: The area under the curve is negative, if z value is also negative. True or False?

A:

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: calculate the integral.

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Q: (10) [x sinx dx

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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 the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

Q: Find the area bounded by the curves y=sinx, y=cosx between x=0 and x=π/2. PLEASE INCLUDE HOW TO GET…

A: To find out the area bounded by the curves.

Q: Arcrin x dx

A:

Q: use integration by parts to write the integral sec^7 (3x) dx in terms of integral sec^5 (3x) dx

A: ∫sec7(3x)dxPut 3x=uso 3dx=du=13∫sec7uduNow ∫sec7udu=∫sec5usec2udu

Q: Calculate the area between the curves ² = 16 sin 20 and ²: = 16 cos 20 .Show by drawing

A: Given: The curves r2=16cos2θ , r2=16sin2θ To find: Area bounded by two curves  r2=16cos2θ ,…

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 the definite integral 5 tan(x)dx using strips of width for the trapezium rule correct to three…

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Q: Find the area enclosed by the curve r = 2 sin(0) + 3 sin(90).

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Q: Find the area of shaded region. sin 29 1 2 O A B.

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Q: Evaluate the integral sinx*ln|1+sinx|dx through integration by parts.

A: Let I=∫sinx·ln1+sinxdx. The integration by parts formula is ∫udv=uv-∫vdu. We choose u and dv…

Q: Evaluate π' sin(πα) da

A:

Q: 5. Find the area under the curve integrate 2/(9 - x ^ 2) dx

A: Given;           ∫29-x2 dx Take the constant out: ∫a.fx dx=a.∫fx dx           =2.∫19-x2 dx Apply…

Q: Use integration by parts to evaluate the integral. sin(In(5x))dx

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Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

A: We have given the curve, y = 3 + 1/2 cosh x   ; 0&lt;=x &lt;=1

Q: Use trigonometric techniques of integration to evaluate tan12x sec x dx tan15x tan13x + C

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Q: sin' (2x) cos (2x)dx =

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Q: The definite integral that calculates the area of the shaded region is given as: yA y 1

A: use the application of integral to solve for the area

Q: Use integration by parts for both.

A: The given integral is

Q: Find area of circle whose eq is (x-3)^2 - (y-3)^2=4 using integration

A: Note: The correct equation of circle will be x-32+y-32=4.  The radius of the circle is 2 and center…

Q: Integrate using trigonometric substitution Integral of x/(x^2-1)dx

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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.