Find the are length of the curve x = (y² + 2)/2 from y-0 to y=1

Q: The line y = 3x + k is tangent to the curve y = x when k is equal to

A: Given,        The line y=3x+k is tangent to the curve y=x3

Q: Find an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

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Q: The cubic y = ax3 + bx? + cx + d tangent to the line y = 12x + 13 at (-1, 1) and have a horizontal…

A: Solution...

Q: Find an equation of tangent equation is 2x+6y=3. line to the graph of y=x+lax that is perpendicular…

A: We need to find the equation of the tangent line to the graph y=x+ln(x) that is perpendicular to the…

Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

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Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

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Q: FIND THE LENGTH OF THE CURVE y = In sec X from X = 0 to X = - 4

A: Given curve is y= lnsecx .  We have to find the length of the curve from x=0 to x=π4. Length formula…

Q: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

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Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the exact length of the curve. y = 7+ cosh (2x), 0 ≤ x ≤ 4 1 2

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Q: Consider the curve defined by the equation y3+xy+2=0.  Show that there are no points on this curve…

A: Consider the given curve define by the equation:

Q: Find the exact length of the curve. = 글Vy (y-3), 16 sys 25 X =

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Q: to the curve y = F(x) at the point with x %3D

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Q: 1 Find the length of the curve x= from y 1 to y=2. +. 16y

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Q: Consider the curve defined by the equation y³ + xy + 2 = 0. Show that there are no points on this…

A: Given Equation of curve   y3+xy+2=0  ---(1)

Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: x = e' and y = te %3D

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Q: Find the exact length of the curve.   36y2 = (x2 − 4)3,    5 ≤ x ≤ 6,    y ≥ 0

A: NOTE: Refresh your page if you can't see any equations. . but here

Q: Find the exact length of the curve. 36y2 = (x2 – 4)³, 4 < x < 9, y 2 0

A: Given:

Q: Find the exact length of the curve over the given interval. 1 along 1 < y < 2. 8 4y2 ' ||

A: Find the length of the given curve

Q: X = 8 1 + 1 < y< 2 4y2'

A: We find the length of the given curve by using the formula of length of the curve. The length of a…

Q: Find the exact length of the curve. X = 8. 1sys 2 4y2'

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Q: Find the length of the curve y = In(1 – x), 0sxs.

A: Given: y=ln(1−x2)0≤x≤12

Q: Find the exact length of the curve. 1 1sys 2 4y2' X =

A:

Q: Find the exact length of the curve. 1 y = 3+ cosh 2x, 0<1<1 2

A: we need to evaluate the Length of curve where  0 ≤ x ≤ 1

Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

A:

Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t = 0 to t = 3.

A: To find the length of the curve parameterized by x=2+3t2 and y=3+2t3 from t=0 to t=3.

Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

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Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: + 2 Find the length of the curve y = from the point where a = 1 to the point where x = 2.

A: The length s of a curve with the function y=f(x) for the interval of x from a to b is given by the…

Q: Evaluate the length of the curve: y = 3x + sinx, 0 ≤ x ≤ 1.

A: Let L be the length of curve  F(x) = 3x + sinx

Q: 1. Find the are length of the curve x = (y + 2)2 from y-0 to y=1

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

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Q: Find the exact length of the curve. 1 + 8. X = 1 s y < 3 4y2'

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Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

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Q: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

Q: s to the curve y = x* at the %3D

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Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

Q: Find the exact length of the curve. y = 4 글2-글 In(x), 1 < x < 4

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Q: Find the length of the curve. 33) y-승. from x = 1 to x= 5 2x

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Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: find the under the curve y=7-t^2 and above the t-axis

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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.