Question 1.
Solve \int_0^3 (x^2+1)dx with Composite Simpson's 1/3 Rule for $n=4$ subintervals.
Question 2.
f(0)=0, f(2)=0.034921, f(4)=0.06993.
Fit f(0)=0, f(2)=0.034921 and f(4)=0.06993 to a curve using Lagrange interpolation. Calculate f(1) and f(5)
using the curve equation you obtained.
Question 3.
The upward speed of a rocket is calculated by the formula
$V = u \ln(\frac{m}{m-qt}) - gt$
$V = 1000\frac{m}{s}$, $u = 2200\frac{m}{s}$, $m_0 = 160000 kg$, $q = 2680 \frac{kg}{s}$, $g = 9.81 m/s^2$
Find the value of t between 15 and 40 using the midpoint method with a relative percentage error $|e| < 3\%.$