M=\frac{2 \pi a b}{c^{2}} \int_{0}^{2 \pi} \frac{\cos (x)}{\sqrt{h^{2}+a^{2}+b^{2}-2 a b \cos (x)}} d x The mutual inductance between two circles of radii a and b, with their centres a distance h apart is given by the integral This integral cannot be evaluated using standard integrals and so numerical techniques are necessary. Consider the integral I=\int_{0}^{2 \pi} \frac{\cos (x)}{\sqrt{6-2 \cos (x)}} d x Working to 6 decimal places, complete the following table of values for f(x)=\frac{\cos (x)}{\sqrt{6-2 \cos (x)}}

Estimate this integral using i) Trapezium Rule ii)Simpsons Rule.