Q3/ Find the shared area between the circle r = (2N sin 0) and the curve r N + sine. N=2*

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 + 1 y = y 6 4 -1 1…

A: y=23x2+132 Differentiating with respect to x, we get dydx=23·32x2+132-1·dx2+1dx=x2+112·2x=2xx2+112

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 arc length of the graph of the function over the indicated interval.

A: Using the power rule we find the derivative of y

Q: Find the arc length of the graph of y = ln(sin x) from x = π /4 to x = π/2.

A: The formula to find arc length of a curve f(x) from x=a to x=b is, L=∫ab1+f'(x)2dx.

Q: Find the arc length of the graph of the function over the indicated interval. Express the result as…

A: Here we have to use the basic formula to find arc length which is shown below and use basic…

Q: Find the arc length of f(x) = (1+2²) from x = 0 to x = 2. Simplify your

A: Given :fx=231+x232x from 0 to 2

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A:

Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8 %3D…

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Q: Find the the arc length of y = 3x² – 2 from x = 0 to x = 4 No decimal entries. Find the exact value.…

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Q: • Find the arc length of the curve from point P to point Q. • Show all work and use proper notation…

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Q: Find the arc length of the graph of the function y=ln(cosx)y=ln(cosx) over the interval…

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Q: what is the arc lenght of  the curve y=ln(sinx) between th points x=pi/3 x = 2pi/3 ?

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Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 & x2=8

Q: Find the arc length of the curve x = -2y³/2 from y = 0 to y = 10. Length =

A: The given curve is x=-2y32 from y=0 to y=10. Find the arc length. As we know the formula of arc…

Q: Find the exact arc length of the curve over the stated interval. Y = 5x³/2 2. from x = 0 to x = 1…

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Q: the length of the curve y = coshx 1sx<2 is sinh(2) – sinh(1) Select one: O True O False

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: 1. Find the area under one arch of the curve y = cos- :cosex.

A:

Q: 6) Find dr at r = 0 where y = arctan(arcsin(x) + 4) + 3x² – 3. Would it make sense to try to dy find…

A: Given data: The given expression is y=arctan(arcsin(x)+4)++3x2-3. The derivative of the given…

Q: Find the exact arc length of the curve. x6 + 8 y = from x = 1 to x = 3. 16x2 Give the exact answer…

A: To Determine: find the exact arc length of the curve  Given: we have a function y=x6+816x2…

Q: Find the area between the inner and outer ovals of r = 4(1+sine

A: I am going to solve the given problem by using some simple calculus to get the require

Q: Find the arc length of the curve x -3y3/2 from y = 0 to y = 10. Length

A: Integration √1+(f'(y)) 2dy

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

A:

Q: Find the arc length of the graph of the function y = ln(1 − x2 ) on the interval 0 ≤ x ≤ 1/2

A: Given:            y= ln 1-x2,  0≤x≤12    Formula to be used: Let y=f(x) be differentiable function…

Q: Find the arc length of the graph of the function over the indicated interval. x= =cy² + 2)3/2, 0sys2

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . 4

A: Given that, y = ln(cosx) To find length of curve, we have formula Length of curve = ∫ab1 + [f'(x)]2…

Q: Use the trapezoidal rule with n = 5 to approximate cos(x) -dr Keep at least 2 decimal places…

A: The trapezoid rule is

Q: Sketch the regions enclosed by the given curves and find its area. Thank you. y = 4 cos(7x),   y =…

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Q: Find the arc length of the graph of the function over the indicated interval.

A: Differentiating with respect to x, we get

Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: rea of the region between the sine curve

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: Find the length of the curve y = = cosh(x), 0 < x < 1. Arc length =

A: Arc length of a curve y=f(x) on [a,b] is given by, L=∫ab1+y'2dx ddxsinh(x)=cosh(x)…

Q: Find the arc length of the graph of y = √(16 − x2) over the interval [0, 4].

A: Given: y=16-x2 interval [0, 4]

Q: Find the exact length of the curve. y = 6 + cosh(3x), 0s x 8 중이nh(3) sinh(3)

A:

Q: Find the arc length of y = ²√x(3-x) for 0 ≤ x ≤ 3. - Express your answer in decimal form rounded…

A: Given problem:- Find the arc length of y = (1/3)√x(3-x) for 0 ≤ x ≤ 3.

Q: Find the length of the arc of the curve y = ln x over the interval: 1, 7| . Round the answer to four…

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Q: Find  the Arc length of the graph of y=Ln(cosx) from x=0 to x=π/4

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Q: What is the lenght of the arc of the circle r = sin 0 that remains outside of the cardioid r =1- sin…

A: The graph is as follows

Q: ind the length of arc of the curve 6xy = x⁴ + 3, from the point where x = 1 to the point where x =…

A: Here given equation as 6xy=x4+3ory=16x3+3x Differentiate with respect to x…

Q: Use the trapezoidal rule with n = 8 to approximate %3D cos(x) Keep at least 2 decimal places…

A: We have to find the value of the integral∫16cosxxdx using trapezoidal rule with n=8. From…

Q: Find the arc length of the functionf (x) from.x = 0 tox = 2. f (x) = sinx Round your answer to three…

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Q: 2. Find the arc length of the curve y = 16 from x=2 to x-3 2x

A: Given y=x416+12x2, x=2 to x=3

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 x2 + 1 y = y

A: Here we need to find arc length of y from x=0 to x=1

Q: Find the arc length of f(x) = In(sin(x)) for - 10 8

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Q: Find the arc length for y = In(sinx) on [4' 4

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Find the arc 3/2 y= 2x length 1 15x52 of on

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Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A:

Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8 %3D…

A: The curve is y=8x2/3

Q: Find the length of the arc of the curve y = (1 + x²) fron the point where x = 0 to the point where x…

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.