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Function from Arc Length

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Wize University Calculus 1 Textbook > Applications of Integration

Arc Length

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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

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.
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.
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)
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].