Unable to solve the definite integral

Questions
,
1

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.

2

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)
3

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