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Unable to solve the definite integral

Posted 3 years ago

indefinite integral of

Integrate[a^(-m/2),a]

is

-((2 a^(1 - m/2))/(-2 + m))

However, I am not able to get the definite integral of the same.

Integrate[a^(-m/2),{a,a0,af}]

Don't know the reason? Manually it's very easy.

POSTED BY: KRISHAN SHARMA
2 Replies

The key is to give Mathematica clues about the constants. For example, if m>0 then a^(-m/2) has an asymptote at a=0. You can give Mathematica information about the constants using the Assumptions option. For example, if 0 < a0 < af, then Mathematica does not have to worry about a possible asymptote at a=0:

Integrate[a^(-m/2), {a, a0, af}, Assumptions -> 0 < a0 < af]

This quickly returns the value:

(2 (a0^(1 - m/2) - af^(1 - m/2)))/(-2 + m)
POSTED BY: Michael Harrison
Posted 3 years ago

Thank you, Michael :) Actually I am new to Mathematica. Nicely explained, it cleared my doubt.

POSTED BY: KRISHAN SHARMA
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