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10: Integrate a function

Only Mathematica and Maple can integrate symbolically.
All four can do numerical integration on ``nice'' functions, but
Mathematica and Maple are more reliable for functions that are not so nice.

1. integrate sqrt(2+sin(x)) from x=1.1 to x=3.3
2. integrate sqrt(2+sin(x)) from x=a to x=b
3. indefinite integral of sqrt(2+sin(x))

Mathematica:

Integrate[ Sqrt[2+Sin[x]], {x,1.1,3.3} ]
Integrate[ Sqrt[2+Sin[x]], {x, a, b} ]
Integrate[ Sqrt[2+Sin[x]], x ]

Matlab:

syms x a b
int(sqrt(2+sin(x)), x, 1.1, 3.3)
int(sqrt(2+sin(x)), x, a, b)
int(sqrt(2+sin(x)), x)

Maple:

value(Int(sqrt(2+sin(x)), x=1.1..3.3));
value(Int(sqrt(2+sin(x)), x=a..b));
value(Int(sqrt(2+sin(x)), x));

IDL:

does only numerical integration (#1), not analytic (#2,#3).
First define function ``myfunc'', then use QSIMP:

function myfunc, x
    return, sqrt(2.0+sin(x))
end

print, QSIMP( 'myfunc', 1.1, 3.3 )