(adsbygoogle = window.adsbygoogle || []).push({}); Is this right?

1. The problem statement, all variables and given/known data

Hello , so in spivak's calculus we only learn to calculate the integral of x^2 and x in the first chapter , i was wonderin gwhat would the integral of ##x^(1/2)## ##\int_a^b##x^(1/2)## ~dx## , well i used the inverse function and a little bit of work i calculated from 0 to 2 using the integral of x^2 on 0 to 2^(1/2) and integral of 2^(1/2) on 0 to 2 turned out it's the correct answer using wolfram alpha , i checked other variables same , so i tried to generalize this , i don't know if this is correct but here it is (f-1 = f^-1 inverse function of f , it wouldn't let me write it on latex)

##\int_a^b f(x)~dx##=-##\int_c^d f^-1(x)~dx##+##\int_a^b f(b)-f(a)~dx##

where c = f^-1(a) and d=f^-1(b)

i didn't check for a lot of functions , but i was wondering if this is right ; thanks everyone :).

**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!

# Is this right?(something i discovered )

Loading...

Similar Threads - right something discovered | Date |
---|---|

Can not get Integral Right | Feb 10, 2014 |

Is my conception/ knowledge about calculus right? | Oct 16, 2013 |

Can't decide if my proof is right or not ?inverse functions | Jul 24, 2013 |

Why is the right hand rule for cross product? | Jul 16, 2013 |

Fundamental theorem of calculus (something isn't right) | Feb 12, 2010 |

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