00:01
Hello everyone, we have a question in which we have given a curve x equals to y raise to the power 3 upon 2 divided by 3 minus y raise to the power 1 divided by and in this question we have to find the length of this curve from y equals to 5 to y equals to 10.
00:28
So the length of the curve will be given as integration of under root 1 plus d x over dy whole square dy and we will take a limit y1 to y2.
00:48
So now we will use this formula to find the length of this curve.
00:54
So now we will put the values in this formula then we will get integration the value of y1 is 5 because the lower limit is 5 and the upper limit is 10 so the value of y 2 will be 10 under root 1 plus differentiation of x with respect to y the value of x is this so now we will differentiate this function with respect to y it will be 1 divided by 3 multiply by 3 divided by 2 multiply by y raised to the power 1 by 2 minus 1 divided by 2 multiply by y raise to the power negative 1 by 2 right and whole square of this derivative now that will be equal to integration of 5 to 10 under root 1 plus this 3 will be cancelled with this 3.
02:00
And we are left with 1 divided by 2, virus 3 power 1 by 2 minus 1 divided by 2 and virus 3 power negative 1 by 2 and whole square of this function.
02:18
Now you can see that we have 1 divided by 2 common in this function.
02:23
So we will take 1 by 2 as common and we have already square of this whole function.
02:30
So we will take the square of 1 by 2 as common.
02:35
So that will be equal to integration of 5 to 10 under root 1 plus, then we will take 1 by 2 as common.
02:46
So the square of 1 by 2 will be 1 by 4.
02:50
Multiply by 1 .1 .5.
02:54
Minus y -restri power negative 1 divided by 2 and divide...