factorize the constant
can you handle this
how do you solve these questions:
1. find the arc length of Y^3= 8X^2 from x=1 and x=8.
my working: ( i know how to form the equation for intergration but i do not know how to carry out the intergration)
differenciating the qns, i got 3y^2 (dy/dx) = 3/4 X ^(1/3)
then i would like to intergrate ( 1 + (9/16 X ^(2/3)))^(1/2) dx from x=8 to x=1.
but im stuck now..how do i perform intergration on this equation?
2.find the arc length of 6xy = x^4 + 3
by implicit differentiation, i got
(dy/dx)^2 = ( 5/6x^2 + 1/ (2x^2))^2
and then i would have to perform intergration on
(1+ (dy/dx)^2 ) ^(1/2) from x= 2 to x= 1...
but i am stuck as to how i should carry out the intergration.
and that's when I thought of it.
If you let and pick p and q to match the powers. Here and work! Also note that when then and then . Then it's a matter of assembling the arc length formula
then we can use the sub .
Using the original formula in terms of x works (as Soroban shows) but I think is a little more difficult.