Can someone check my working to see if this is correct for both questions?
Estimate: ∫(2,0) 1/1+x^2 dx
i) Using the Mid-Ordinate rule with 4 strips
ii) Using Simpson's rule with 4 strips
i) h=b-a/n
= 2-0/4 = 0.5
x 0 0.5 1 1.5 2
y 1 0.8 0.5 0.308 0.2
=h(y1+y2+y3+...yn)...
Can someone check this is correct?
Using the Newton Raphson method with X0=2 to find the root of the equation:
x^3-x-1=0 (correct to 4.d.p)
My answer is:
f'(x)= 3x^2-1
xn+1= 2-x^3-x-1/3x^2-1
xn+1= 2-2^3-2-1/3(2^2)-1
x1= 17/11
x2= 17/11-(17/11^3)-17/11-1/3x(17/11^2)-1
= 1.3596