Arc Length of the curve

Question

Find the arc length of the curve y= x³/3 + 1/4x x=1 to x=2

Answer 1

Y = (X^3)/3 + X/4 from X = 1 to 2

As per formula of Arc Length( S) we have:

ds = SQRT(1 + (dy/dx)^2) dx from x = 1 to 2; In our case dy/dx = X^2 + 1/4 ;

I have used TI-84 plus graphing Calculator; In this Calculator under function MATH there is another function called fnInt to calculate definite Integration .

Hence S = Integration of ( SQRT(1+ (dy/dx)^2) dx from x = 1 to 2 will give 2.789407......

Answer 2

dy/dx = x^2 + 1/4

sqrt( 1+ (x^2+1/4)^2) must be integrated numerically from 1 to 2

Simpson's Rule with 10 steps gives an approximation of 2.78940761157427