# Numerical Integration

It is required to use the Trapezium's rule to evaluate the integral of sin(x)^2 from 0 to pi/2 to four decimal place accuracy. Use the error bound formula to recommend the number of panels n.

Find the Trapezium rule approximation of the integral with n=2 and compare with the exact value. Does this result contradict your part (a) answer?

The initial-value problem is given by dy/dx=x+sqrt(y) , y(0) = 1.

Use Runge-Kutta's method with step size h = 0.1 to find the value of y(0.1) correct to 3

https://brainmass.com/math/integrals/numerical-integration-trapezium-rule-error-bound-formula-95824

#### Solution Summary

This problem illustrates the use of Trapezium rule to evaluate a definite integral and estimating the error in using trapezium rule. It is then compared with the Runge-Kutta Method

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