Question

Check my work: Arc Lengths

Answer 1

Derivative of x^3/3 + 1/4x^2 = x^2 -1/4x^2
Derivative squared:x^4 + 1/16x^4 -1/2

Answer 2

Derivative squared +1: x^4 + 1/16x^4 -1/2 + 1 = x^4 + 1/16x^4 +1/2
Square root: sqrt( x^4 + 1/16x^4 +1/2) = x^2 +1/4x^2 + 1/sqrt(2)

Answer 3

correct process.

Answer 4

\[\int\limits_{1}^{2} x^2 +1/4x^2 + 1/\sqrt(2) = 59/24+1/\sqrt(2)\]

Answer 5

answer is correct.

Answer 6

Problem is, the answer is just 59/24.

Answer 7

!!!

Answer 8

I don't see how I got that 1/sqrt(2) part wrong. My mathbook says it's just 59/24.

Answer 9

second part may be missing fm book. May be printing mistake.

Answer 10

@sirm3d , do you see what I did wrong?

Answer 11

i'm still checking.

Answer 12

Thanks!

Answer 13

\[\sqrt{x^4-\frac{1}{2}+\frac{1}{16x^4}+1}=\sqrt{x^4+\frac{1}{2}+\frac{1}{16x^4}}=x^2+\frac{1}{4x^2}\]

Answer 14

\[\Large L=\int_1^2 x^2+\frac{1}{4x^2} \;\mathrm dx\]

Answer 15

Okay, that makes sense. Thanks!

Answer 16

yw