00:01
In this question, we are asked to write down the formulas for the arc length of the given functions, and then use a calculator to calculate the integrals.
00:11
So the arc length equals, in the first case to the integral from 0 to 3, of the square root of 1 plus f prime of x squared d x, where f prime of x is the derivative of the function f and equals to 2 times e to the 2x, and that means that f prime squared of x equals to 4 times e to the 4x and then the arc length equals to the integral from 0 to 3 of the square root of 1 plus 4 times e to the 4x dx.
01:00
To calculate this integral i will use wolfram alpha so we will ask it to integrate the square root of 1 plus 1 plus 4 times e to the 4x from 0 to 3.
01:36
So yeah, i think that's what we're asked to calculate and the integral approximately equals to 402 .55.
01:49
Alright, that's the value, the arc length of the first curve.
01:53
Now let's move on to the next one.
01:56
It's the arc length of sine x squared from 0 to pi.
02:01
The formula is l equals to the integral from 0 to pi...