1) The arc length of the curve y = f(x) Over the interval asx

Q: Find the arc length of y = 3x – 1 on 0 < x < 4. < 4. -

A:

Q: Find the arc length of the graph by partitioning the x-axis.   9y2 = 4(1+x2)3 , from x=0 to x=4√2…

A: Given: 9y2=4(1+x2)3  from x=0 to x=4sqrt(2)

Q: Find the arc length of the catenary y = coshx between x 0 and x = In4.

A: we'll allow providing one solution at a time. Please submit the rest questions separately.   Given:…

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x312 from (0, 0) to (4, 8)

A:

Q: What is the arc length of the curve y = (2/3)(x-4)3/2 from the point where x = 4 to the point where…

A: Given: y=23(x-4)32

Q: Find the arc length function for the graph of ƒ(x) = 2x^(3/2) using (0, 0) as the starting point.…

A: Given:

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 y³ + y = x² + 6x on the interval [-5, –1].

A: Since the given graph is in implicit form (we can not find the explicit value of y in terms of…

Q: Evaluate [12x. (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A:

Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: calculate the arc length over the given interval. y = 4x − 2, [−2, 2]

A:

Q: From Rogawski ET 2e section 8.1, exercise 9. Calculate the arc length of y = - x - In x over the…

A:

Q: Find the arc length of the graph of y == 6 2x on the interval 2 L2

A:

Q: Find the arc length function for the curve y = sin(x) + /1 - x2 with starting point (0, 1). s(x) =

A: To find the are length,  we will use the formula of are length (S) .

Q: Find the arc length of f(x) = In(cos x) on- %3D 4

A:

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

A:

Q: Find the arc length function for the curve y = sin+(x) V1-x² with starting point (0, 1).

A: As we know that; The expression for the length of arc of the curve is: L=∫ab1+dydx2dx The Power…

Q: Find the length of the arc of the curve y =: +e*) from x = 0 to x =2.

A: y=ex+e-x2

Q: Find the arc length of the following curve on the given interval by integrating with respect to x. y…

A:

Q: Find the arc length function for the curve y = sin-lx + V1 - x² with starting point (0, 1).

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2 for 2≤x≤6 if you integrate with…

A:

Q: Find the arc length s of the curve y= x2 on the interval  [0,2]

A: The objective of the question is determine the arc length of the given function.

Q: Find the arc length function for the curve y=  sin inverse x  + sqrt ( 1 - x sq. ) with starting…

A:

Q: Calculate the length of arc of y = 2x/² for 0≤x≤1

A:

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Find the arc length function for the curve y = 2x/2 with starting point Po(25, 250). s(x) =

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 y 4x – 1 on 0 < x < 2. -

A:

Q: Find the arc length of the catenary y = cosh x between x = 0and x = ln 2.

A: Given y=cosh(x)

Q: 1. f (x) = cosh x on [0, 1] %3|

A:

Q: Find the arc length of the graph of y = -- 2 over (0,4].

A:

Q: Find the arc length of the curve y = log(1/cosx) from x = (/4) tox= (/3)

A:

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A:

Q: 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

A:

Q: - Find the arc length of f(x) = (-) (x² + 2)ž on the interval [0,9)

A:

Q: Compute the arc length of y = ln(x) – (1/8)x² on 1< < 3

A: Arc length:       Arc length is the distance between two points along a section of the curve.  Let…

Q: 5. Compute the arc length exactly y =x² -In x , 1 sx< 2

A: Given : y=14x2-12lnx , 1≤x≤2   To Find: Arc length

Q: Set up an integral to find the arc length of the curve defined by  x = tany  on the intergral 0 ≤ y…

A:

Q: Estimate the arc length from point (0,0) to (1,1) on the graph of y = x² using the Composite…

A: arc length  of the curve y=f(x) from x=a to x=b  L=∫abds  where ds=dx2+dy2=1+dydx2dx Integral have…

Q: Find the exact arc length of the curve over the stated interval. = 3x3/2 – 2, from x = 0 to x = 1…

A: We have to find the arc length of the curve over the stated interval.…

Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

A:

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 segment of curve y = In(cos x) for 0< x<"/3. DO NOT integrate in your…

A:

Q: Find the arc length of the curve y :In(cos x) from x = 0 to x = t/3. Length:

A:

Q: Find the arc length from x=0 to x=100 of the catenary: 150cosh(x/150)

A:

Q: Calculate the arc length of y = - x² - In x over the interval [1, 8e]. %3D

A:

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

A:

Q: 1 Find the arc length of the curve y = + 4 from (0, 4) to (1, ).

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.