If f(x) = 3x^2/3 − 10, find the arc length of the graph of f from the point A(8, 2) to B(27, 17).

Q: To find the length of the curve defined by y = 5x° + 8x from the point (-1,-13) to the point (2,56),…

A: Here the curve is given by y=5x3+8x x coordinate of the points (-1,-13) and (2,56) are -1 and 2…

Q: Find the slope of the line tangent to the graph of y= sin3x at x=pie/6

A:

Q: 2x2 dx 5 – x²

A: In the given question we have to find the integration by putting in the integral. So we will…

Q: Find the indefinite integral .

A: To find the indefinite integral  I=∫sin-12x1-4x2dx  Let u  = sin-1 2x dudx = 11-2x2du = 11-4x2 dx

Q: The slope of the tangent line to the curve y 2x at the point 2, 16) is:

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

A:

Q: Find length of arc of the curve 9y2=4x3 from the origin to the point (3, 2√3)

A: Given curve is 9y2=4x3, and the point is 3,23.   The objective is to determine the length of arc of…

Q: find the slope of the tangent line to the graph of flx)= 2x at (5,3).

A: NOTE: Refresh your page if you can't see any equations. . to find the slope of the line, take the…

Q: as y y = f(x) (10, 4) Tangent line (4, 2) ive your answer to three decimal places.)

A: G

Q: x*Arcsinxe

A: we have to find

Q: Find the slope of the tangent line at the point P = (1, 1) on the graph of              ex-y = 2x2 -…

A: Given,          ex-y = 2x2- y2    at   P=(1, 1)

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

A:

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: Find the slope of the tangent line to y=3x at x=0.   Show all work please

A: The given equation is y = 3x.Differentiate with respect to x on both sides,(dy/dx) = 3x ln(3).

Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

A:

Q: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

A: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ      ∵cos2x=1-2sin2x=2θ=2…

Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

A:

Q: Find the slope of the tangent line to the circle x2+y2 = 4 at (1,-v3)

A: To find the slope of tangent line to the circle x2+y2=4 first find the derivative dydx.…

Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

A:

Q: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

Q: Find the equation of the tangent line to the curve y = rVI at the point (4, 8). %3D

A: We have to find the equation of tangent

Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

A:

Q: Solve for z. 4 12

A: Solve for x

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

A:

Q: What is the length of the arc y = (2/3)(x2+1)3/2 over the interval [3,6]?

A: We need to compute the length of the arc of the given curve over the interval [3,6]

Q: I am having trouble understanding how to graph triple and double integrals.

A: Draw the region of integration E.

Q: What is the length of the arc y = (x6/6) + (1/16x4) on the interval [1,2]?

A: Given, function and interval

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: The slope of the tangent to y = 2 – x2 at the point (1,1) is

A:

Q: Find the slope of the tangent line to the parabola y= 2 +x−x^2 at the point (0,2).

A: Simply take the derivative of the given equation and substitute the given point.

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Find the length of the arc y = 8. 1 from X = 1 to x = 4. 4x www

A: Given

Q: find the equation of a tangent line for y=arcsin(x/8) at the point (4,π/6)

A:

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

A:

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, ) Hint: you may want to differentiate these…

A: We can prove these by two ways . First is by using derivatives of functions. And second by using…

Q: Prove that the arc y = log secx from les (2+ 3

A:

Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

A:

Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: It is given that the x coordinate increases at a steady 10 m/sec. dxdt=10msec. The equation of…

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

A:

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

A:

Q: Find an equation of the tangent line to the graph of y = arcsin(2x) at the point 2/2 4

A:

Q: Find the length of the arc y =: 8 1 from X = 1 tox = 4. 4x?

A: Graph: Given: y=x48+14x2. So,          y'=x48+14x2' =x32-12x3.

Q: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

A:

Q: The slope of the tangent line to the curve y = 4 X at the point 5, is: The equation of this tangent…

A:

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Q: Find the tangent line to the curve ry = a +y+1 at (3,2)

A: Given data: The expression for the given curve is xy=x+y+1. The given point is (a,b)=(3,2).…

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.