A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the exact length of the curve. y = 2 + 8x3/2, 0 ≤ x ≤ 1.
Solution:
The length of the curve y = f(x) a ≤ x ≤ b is given by:
L = \(\int_{a}^{b}\sqrt{1 + (\frac{\mathrm{d} y}{\mathrm{d} x})^{2}}dx\)
y = 2 + 8x3/2
dy/dx = 8(3/2)x1/2
= 12x1/2
√1 + (dy/dx)2 = √1 + (6x1/2)2 = √1 + 144x
Length of the curve L = \(\int_{0}^{1}\sqrt{1 + 144x}dx\)
= \(\frac{2}{3}.\frac{1}{144}[(1+144x)^{3/2}]_{0}^{1}\)
= \(\frac{1}{216}[(1+144(1))^{3/2} - (1+144(0))^{3/2})]\)
= \(\frac{1}{216}[(145)^{3/2} - (1)^{3/2})]\)
= \(\frac{1}{216}[(145)^{3/2} - (1)]\)
Find the exact length of the curve. y = 2 + 8x3/2, 0 ≤ x ≤ 1.
Summary:
The length of the curve y = 2 + 8x3/2 is L = (1/216)[(145)3/2 - 1]
Math worksheets and
visual curriculum
visual curriculum