Show that if 0 ≤ f' (x) ≤ 1 for all x, then the arc length of y = f (x) over [a, b] is at most √2(b − a). Show that for f (x) = x, the arc length equals √2(b − a).
Want to see the full answer?
Check out a sample Q&A here
Related Calculus Q&A
Find answers to questions asked by students like you.
Q: Find the arc length of f(x) = () (x² + 2)z on the interval [0,9] %3D
A: (6) Given function is fx=13x2+232 and interval is 0,9. We have to find the arc length of fx=13x2+232…
Q: For the function f (x) = 1/4ex + e-x, prove that the arc length on any interval has the same value…
A: Click to see the answer
Q: Express the arc length of the curve y = x4 between x = 2 and x = 6 as an integral (but do not…
A: Click to see the answer
Q: For the function f(x)=1/4e^(−x)+e^x, prove that the arc length on any finite interval has the same…
A: Click to see the answer
Q: Calculate the arc length of y = x² – ; In x over the interval [1, 2e].
A: Click to see the answer
Q: Express the arc length of the curve y = x 4 between x = 2 and x = 6as an integral (but do not…
A: Given y=x4 between x=2 and x=6
Q: Find the arc length of the curve below on the given interval by integrating with respect to x. x3 1…
A: Given the curve y=x33+14x ; x∈1,3
Q: Find the arc length of the curve f = Vx from x = 0 to x = 4.
A: Given that y=fx=x. We have to find the arc length of this curve from x=0 to x=4. Since it will be…
Q: Find the arc length of the curve f = vx from x = 0 to x = 4.
A: Consider the given function. f=x Find the derivative of the function. f'x=12x The arc length formula…
Q: The definite integral that can be used to find the arc length of the curve y =x-2 on the interval…
A: Click to see the answer
Q: Find the arc length of y 4x – 1 on 0 < x < 2. -
A: Click to see the answer
Q: Let C be the curve given by f(x) = cosh x for 0 ≤ x ≤ t, where t > 0. Show that the arc length of…
A: Click to see the answer
Q: Find the arc length of the curve y = (x² – 8 In(x)) from x 2 to x = 5. |
A: Click to see the answer
Q: Compute the trapezoidal approximation T5 to the arc length s of y = tan x over [0, 4].
A: Click to see the answer
Q: For the function f(x) = e* + e-x, show that the arc length on any interval has the same %3D value as…
A: Arc length of the curve
Q: Find the arc length of y = 3x – 1 on 0 < x < 4. < 4. -
A: Click to see the answer
Q: Find the arc length of the curve below on the given interval by integrating with respect to x. 1.…
A: Given the given curve is y=x33+14x and the given interval is 1,4.
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: What does the arc length formula give for the length of the line y = x between x = 0 and x = a,…
A: line y = x between x = 0 and x = a
Q: Find the arc length of the curve defined by y = In x over the interval 1sxse.
A: Click to see the answer
Q: The integral V1 + dx represents the arc length of which curve (for 0<x<1)?
A: Click to see the answer
Q: Find the arc length of y = V1 – x² from x = 0 to x
A: Click to see the answer
Q: 1. Compute the arc length of the curve y = t, over the interval (0 < x < 2). 6 x y
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
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: Find the arc length of f(x) = In(cos x) on- %3D 4
A: Click to see the answer
Q: Find the arc length of the curve: x = 2 sin^-1 (t), y = ln(1 - t^2), over the interval
A: Click to see the answer
Q: 2. Find the arc length of (x+5 y= over the closed interval [-1,4] .
A: Given curve is
Q: For the function f(x) = e* + e*, prove that the arc length on any interval has the same value as the…
A: Click to see the answer
Q: Which of the following integrals represents the arc length of the graph of y=2lnx over the integral…
A: Here we we will find intigral which represents arc length of given graph,
Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).
A: Click to see the answer
Q: 5. Compute the arc length of the curve f (x) =1+In(cos(x)) over the interval from x=0 to X =
A: Click to see the answer
Q: Find the value of a such that the arc length of the catenary y = cosh x for −a ≤ x ≤ a equals 10.
A: Click to see the answer
Q: Consider the part of the helix ~x(t) = (2 cost, 2 sin t, 3t) that is bounded by t = 0 and t = 2π.…
A: We have to find the arc length of above helix
Q: Set up an integral that (if solved) would give the arc-length of the following curve on the given…
A: Click to see the answer
Q: Consider the integral arctan(x)dx where -Is a<bs . Making the substitution u=-2x , determine the…
A: Just I have used the given substitution and find that . Upper bound: u1=π/2 Lower bound: U2=-π/2 And…
Q: 5. Compute the arc length of the curve e f (x) =1+In(cos(x)) over the interval from x=0 to 4
A: Click to see the answer
Q: Find the arc length of the curve y(x) for the interval 1 < x<7 where y = S* Vt² – 1 dt +2.
A: We find arc length of given curve
Q: - Find the arc length of f(x) = (-) (x² + 2)ž on the interval [0,9)
A: Click to see the answer
Q: The arc length of a curve y = g(x) over interval a ≤ x ≤ b is given as: Approximate the arc length…
A: The formula to approximate a definite integral according to Simpson's one-third rule is:
Q: Find the arc length of y³ + y = x² + 6x on the interval [-5, –1].
A: Click to see the answer
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: Find the arc length of y³ + y = x² + 6x on the interval [-5,–1].
A: The arc length, L of a function, x=f(y) in the interval [a,b] is calculated using the formula below.…
Q: Find the arc length of the curve on the indicated interval of the parameter. X = 6t + 5, y = 5t – 4,…
A: Click to see the answer
Q: Find the length of the following three-dimensional curve r(t) = (9+3t,3 – 7t, – 1+ 5t) , for 1sts6…
A: Click to see the answer
Q: Set up the integral used to find the length of the curve y = Vī- z5 on the interval -<zs. Select the…
A: Given, y=1-x5 and interval is -14≤x≤14
Q: find the arc length of the curve on the given interval y = (x2+2)3/2/3 on [0,1]
A: Given curve is: y=(x2+2)323 from x=0 to x=1Heredydx=32(x2+2)12×2x3=xx2+2
Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1].
A: To find the arc length of a function x=fy on the interval c,d use the formula L=∫cd1+fy2 dy. Here…
Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1]
A: Use the formula of arc length to determine its value. Simplify the given function to define a…
Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1].
A: Solution: Given that, y3+y=x2+6x, interval -5, -1 Then, differentiating with…
Q: Find the length of arc of the curve 6xy = x* + 3, from the point where x = 1 to the point where x =…
A: Since you have asked multiple question, we will solve the first question for you. If youwant any…
