During maths class last semester this integral came up in the course of discussion and my lecturer gave a quick outline of how to solve it but I didn't grasp it at the time and we moved on. I'd like to know how to do it though! The integral is:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int sin^{2}(x)[/itex]

The next step was:

[itex]\int sin(x).(-cos(x)')[/itex]

where [itex]-cos(x)'[/itex] denotes the derivative of [itex]-cos(x)[/itex] and the implication was that [itex]sin^{2}(x)[/itex] is the result of applying the chain rule to whatever compound function it is the derivative of. I can't remember the result but further steps were skipped and he jumped straight to the answer at this point.

I'm not sure how to proceed here, because the chain rule implies that [itex]\frac{dy}{dx} f(g(x)) = f'(g(x) . g'(x)[/itex], and in my example [itex]g(x) = x[/itex] and [itex]g'(x) = 1[/itex] which doesn't help me end up with [itex]sin(x)[/itex] as required.

Could anyone poke me in the right direction to solve this? =)

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

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

# Which method of integration for sin^2(x) dx

Loading...

Similar Threads - method integration sin^2 | Date |
---|---|

A Integral equations -- Picard method of succesive approximation | Nov 14, 2017 |

Substitution method for finding an integral's interval changes | Jun 8, 2015 |

How to determine inner and outer radii for 'Washer Method'? | May 18, 2015 |

Computing an integral -- any method | Apr 18, 2015 |

Question about substitution method in integration | Nov 26, 2014 |

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