Question

How do you find the arc length of y=10x+1 over the interval [0,7]???? s=??? can someone help please ?

Answer 1

\[s = \int\limits_{a}^{b}\sqrt{1+[f'(x)]^{2}}dx\]

Answer 2

The arc length formula is\[s = \int_a^b \sqrt{1 + f'(x)^2}dx\]so in this case it's\[s = \int_0^7 \sqrt{1 + (10)^2}dx = \int_0^7 \sqrt{101}dx = 7\sqrt{101}.\]
If you want, you can avoid using integrals in this case because the function is a line. The arc length is simply the distance between\[(0, f(0)) = (0, 1)\]and\[(7,f(7)) = (7, 71):\]\[s = \sqrt{7^2 + 70^2} = 7\sqrt{101}.\]

Answer 3

so did you use the distance formula in there

Answer 4

Yes, I did.

Answer 5

ty