integration in sagemath 8.1
I executed the following,
def integral_R(f,a,b):
from sage.symbolic.integration.integral import definite_integral
return (definite_integral(f,x,a,b)).simplify_full()
alpha = 1/sqrt(3)
H = 2*arcsin(x/(sqrt(1-x^2)))
integral_R(H,0,alpha).n()
and got
1.16869906991626
The same integral in Wolfram Alpha provides
0.38330
By inspection I know that Wolfram is right. What's wrong with sage math in the specific example?