High School
SAT
ACT
University
MCAT
LSAT
DAT

Compute the arc length of the curve f(x)=∫_1^x√t^5-1dt for 1≤ x≤9. Hint: use…

Related Topics

Wize University Calculus 1 Textbook > Applications of Integration

Arc Length

3 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Compute the arc length of the curve f(x)=∫1xt5−1dt f\left(x\right)=\int_1^x\sqrt{t^5-1}dt\ for  1≤x≤9\ 1\le x\le9.

Hint: use the Fundamental Theorem of Calculus: ddx∫cxf(t)dt=f(x)\frac{d}{dx}\int_c^x f(t)dt=f(x)
More Arc Length Questions:
Arc Length
Which of the following integrals represent the arc length of the curve r=sin⁡2(θ4)r=\sin^2\left(\frac{\theta}{4}\right)?
Find the arc length of y=2x32y=2x^{\frac{3}{2}} on [0, 53]\left[0,\ \dfrac{5}{3}\right].
Q:\bf{Q:} Find the arc length of y=2x32y=2x^{\frac{3}{2}} on [0, 53]\left[0,\ \dfrac{5}{3}\right].
Find the arc length of the curve y=3+12cosh⁡ 2xy = 3 +\dfrac{1}{2}\cosh\ 2x from x=0x=0 to x=1x=1.
Function from Arc Length
Find a curve through the point (0,1)(0, 1) whose length integral is L=∫121+1y4 dy\displaystyle L=\int_1^2\sqrt{1+\frac{1}{y^4}}\ dy
Arc Length with Partial Fractions
Find the arc length of y=exy=e^x on [0,1][0,1].
Practice: Arc Length with Perfect Square
Q:\textbf{Q:} Consider the curve y=f(x)=x33+14xy=f(x)=\dfrac{x^3}{3}+\dfrac{1}{4x}. Find the arc length of this curve over the interval [1,3][1, 3]. Find a function giving the arc length of the curve over the interval [1,x].[1, x].
Find the arc length of y=2x32y=2x^{\frac{3}{2}} on [0, 53]\left[0,\ \dfrac{5}{3}\right].
(a) 525\sqrt2 (b) 23\frac23 (c) 143\frac{14}{3} (d) 737\sqrt3 (e) 227\frac{2}{27}
Q:\bf{Q:} Find the arc length of y=2x32y=2x^{\frac{3}{2}} on [0, 53]\left[0,\ \dfrac{5}{3}\right].
Arc Length
Which of the following integrals represent the arc length of the curve r=sin⁡2(θ4)r=\sin^2\left(\frac{\theta}{4}\right)?
Practice Question: Arc Length
Find the arc length function for the curve y=2x3/2y=2x^{3/2} with starting point P0=(0,0)P_0=\left(0,0\right).
Q:\bf{Q:} Find the arc length of y=2x32y=2x^{\frac{3}{2}} on [0, 53]\left[0,\ \dfrac{5}{3}\right].
Find the arc length of the curve y=3+12cosh⁡ 2xy = 3 +\dfrac{1}{2}\cosh\ 2x from x=0x=0 to x=1x=1.
Arc Length with Partial Fractions
Find the arc length of y=exy=e^x on [0,1][0,1].
Function from Arc Length
Find a curve through the point (0,1)(0, 1) whose length integral is L=∫121+1y4 dy\displaystyle L=\int_1^2\sqrt{1+\frac{1}{y^4}}\ dy
Practice: Arc Length with Perfect Square
Q:\textbf{Q:} Consider the curve y=f(x)=x33+14xy=f(x)=\dfrac{x^3}{3}+\dfrac{1}{4x}. Find the arc length of this curve over the interval [1,3][1, 3]. Find a function giving the arc length of the curve over the interval [1,x].[1, x].