Hello, I am having trouble understanding a question in relation to Euler's method.(adsbygoogle = window.adsbygoogle || []).push({});

Basically, the question goes something like Euler's method is solved to solve the differential equation [tex]\frac{{dy}}{{dx}} = \log _e \left( {4 - x^2 } \right)[/tex], with a step size of 0.05 and initial condition y = 0 when x = 0. Let A be magnitude of the area enclosed by the curve [tex]f\left( x \right) = \log _e \left( {4 - x^2 } \right)[/tex], the coordinate axes and the line x = 1. Why is [tex]y_{20}[/tex] an estimate of A?

Answer: [tex]y_{20} \approx \int\limits_0^{x_{20} } {\log _e \left( {4 - x^2 } \right)} dx = \int\limits_0^1 {\log _e \left( {4 - x^2 } \right)dx} = A[/tex]

I do not understand the answer. As far as I understand, [tex]y_{20}[/tex] is just the value of the antiderivative at x = 1, given initial conditions but the answer does not make use of the initial conditions. I do not see how [tex]y_{20}[/tex] can be considered to be an approximation of A if the initial conditions are not used.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Euler's method

Loading...

Similar Threads for Euler's method | Date |
---|---|

B Euler's method for second order DE | Oct 4, 2016 |

Help with implicit euler method | May 27, 2014 |

Midpoint Euler method, second order system | Jun 12, 2013 |

Backward euler method for heat equation with neumann b.c. | Mar 17, 2013 |

**Physics Forums - The Fusion of Science and Community**