I often have trouble getting Wolfram|Alpha to compute definite integrals with variable bounds, and I'm wondering whether I'm missing something.
Some examples: $\int_a^b \sin x\mathrm dx$ and $\int \arcsin x \mathrm dx$ work fine; $\int_0^a \arcsin x \mathrm dx$ already requires extra time to finish; and $\int_a^b \arcsin x \mathrm dx$ doesn't compute even with extra time.
I'm thinking it probably has something to do with the conditions on the bounds, since there are conditions for the arcsine but not for the sine. It could be that W|A is having a hard time figuring out the conditions by itself; if so, how could I help it along?
Best Answer
Yes, in Mathematica directly specifying conditions reduces computation time and sometimes allows to obtain a result at all. Mathematica input
Integrate[ArcSin[x],{x,a,b},Assumptions->{-1<=a<b<=1}]gets a result, but somewhat strange one, the integral is considered as indefinite.