1 + 3 x2 y 4x

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

Q: Find the exact length of the curve. x = 6 + 3t, y = 9 + 2r, 0sts 5

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Q: Find the length of the curve y = 3/2 from a = 0 to a = 3.

A: Given curve is y=43x32   Length of the curve is L=∫ab1+dydx2      ......1 Here given a=0 and b=3 and…

Q: Find the exact length of the curve. y = 5 + 2x3/2, 0≤x≤1 2.2683 X

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Q: Use the guidelines of this section to sketch the curve   y =x/  sqrt( x2   +1)

A: This function can not have the denominator equal to 0, so there will be no vertical asymptote.

Q: Find the exact length of the curve. x = 7 + 12t, y = 5 + 8t, 0sts 4

A: Given :      x=7+12t2 ,y=5+8t3 ,  0≤t≤4

Q: Find the exact length of the curve. y = 4 + 6x3/2, 0 < x < 1

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Q: Find the exact length of the curve. y = 4 + 4x3/2, osxS1

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Q: Find the exact length of the curve. x = 4 + 9t2, y = 3 + 6t, 0stsi

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Q: Find the exact length of the curve. y = 4 + 8x3/2, Osxs1

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Q: Find the exact length of the curve. y=3+8x3/2, 0 less than or equal to X less than or equal to 1.

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Q: Find the exact length of the curve. Ex372, 0sxs 4 y =

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Q: Find the exact length of the curve. y = 5 + 8x3/2, osxs1

A: Given: y=5+8x32,   0≤x≤1

Q: Find the exact length of the curve. x = 8 + 9t?, y = 3 + 6t, 0 sts4

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Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

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Q: Find the exact length of the curve. x = 6 + 12t2, y = 8 + 8t, 0sts1

A: If x=f(t), y=f(t) on [a,b] then length of curve is L=∫abdxdt2+dydt2dt

Q: Find the point on the curve 4x

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Q: Find the exact length of the curve y=1+6x% for 0<xsl

A: We have to find the exact length of the curve y=1+6x32 for 0≤x≤1.

Q: Find an equation of the line which is tangent to the circle r +y - dr + by – 12 = 0 at the point (5,…

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Q: Find the exact length of the curve. x = 3t2, y = 2t3 ;0 <t<2

A: Given data:     The first parametric equation is: x=3t2. The second parametric equation is: y=2t3.…

Q: Find the exact length of the curve. y = (1 + x2)3/2, 0 < x < 2

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Q: Find the exact length of the curve. x = 2 + 3t2, y = 5 + 2t3, 0sts 2

A: Given,

Q: Find the slope of the tangent to the curve. (If an answer is undefined, enter UNDEFINED.) 2x2 - 10x…

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Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: Find the exact length of the curve. x = 8 + 12t2, y = 9 + 8t³, 0 st< 3

A: given parametric equation of curvex = 8+12t2 ,   y = a+8t3

Q: Find the exact length of the curve. 1 1<x<2 y = 8. 4.x *

A: solution.

Q: Find the exact length of the curve. y = 4 + 4x3/2, oSxS1

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Q: y = 2x-3 2 x² + 4

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Q: Find the exact length of the curve y=x^4/4+1/(8x^2 ) , 1≤x≤2.

A: Given: The expression to calculate the length of a curve 'y=f(x)' is over the interval [a,b] is,…

Q: Find the exact length of the curve. + 4х 1 < x < 3 y

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Q: No calculators. Find the exact length of the curve. 0≤x≤l y=2+2x³/2,

A: Length of the curve  =∫ab 1+f'(x)2 dx .

Q: Find the exact length of the curve y=x3/3 + 1/4x, 1 less than or equal to X less than or equal to 2

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Q: Find the exact length of this curve : to y= 16 2x² |<x<2

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Q: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

Q: Find the equation of the circle, in general form, that is tangent to the line X=−6 andX=10, and…

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Q: Find the exact length of the curve. 1 y = + 10x37 6 1 ≤ x ≤ 3

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Q: Find the exact length of the curve. X = 3 + 6t2 y = 5 + 4t3 0 <ts 3

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Q: Find the lengths of the curves y = 2/3 x3/2 - 1, 0 ≤ x ≤ 1

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Q: Find the length of the curve 3 y = x7 – 2 from x = 0 to X = 4.

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Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 5< xs 6,

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Q: Find the exact length of the curve. = 3/²/₁ y 1 4x 1 ≤x≤2

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Q: Find the exact length of the curve. 23/2 12, 0 <x < 1 y =

A: Given : y=23x32,       0⩽x⩽1   To find : Curve length

Q: Find the exact length of the curve. X = 4 + 6t2, y = 8 + 4t3, 0sts 2

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Q: i) Find the exact length of the curve y=+15x52 4x3 1 ≤ x ≤ 2,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the equation of the family of curves whose slope at any point (x, y) is 2. y 4. equal to the…

A: We need to find the family of curves. NOTE - As per our guidelines we can not solve multiple…

Q: Find the exact length of the curve. x = 1 + 12t2, y = 4 + 8t3, 0 sts 3

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Q: Find the exact length of the curve. 1 y = 1 < x < 2 4x

A: The given curve,   y=x33+14x, 1≤x≤2

Q: Find the length of the curve y = x2, 0 &lt;=x &lt;=sqrt(3)/2.

A: Given information:

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.