00:03
Alright, we have to calculate the length of the arc using simpson's method, okay, and the n given to us is 10.
00:13
So let's see the function given here is actually y is equals to ln 1 plus x cube where x is less than 5 and greater than equals to 0.
00:27
Okay so let's first get the first derivative of this curve because that will be required so the differentiation of the first derivative of this curve is first differentiate the ln so that will be 1 plus x cube and then differentiate 1 plus x cube so differentiation of that will be 3 x squared okay so that is the first derivative now let's write down the formula for length of the curve so length of the curve will be equal to i'm calling that as l here, integration, lower limit which is zero here and upper limit which is 5 here, 2 tower, 1 plus first derivative whole square, okay, here.
01:11
The first derivative is this, whole square of that will be 9 x x to power 4 divided y, 1 plus x cube and square of them into b of x.
01:29
So that will be the length of the curve using this formula.
01:31
And if we calculate it by using the calculator, it is coming approximately 7 .11882.
01:45
Okay? because we have to compare the values in the question as well...