Tutorial 6 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"GlobalAdaptive", Method -> "ClenshawCurtisRule"}]//InputForm

Output

InputForm[2.]

Step 2

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"LocalAdaptive", Method -> "ClenshawCurtisRule"}]//InputForm

Output

InputForm[2.]

Step 3

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> "LobattoKronrodRule"]//InputForm

Output

InputForm[NIntegrate[1/Sqrt[x], {x, 0, 1}, Method -> LobattoKronrodRule]]

Step 4

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"GlobalAdaptive", Method -> "LobattoKronrodRule"}]//InputForm

Output

InputForm[2.]

Step 5

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> "MonteCarloRule"]//InputForm

Output

InputForm[NIntegrate[1/Sqrt[x], {x, 0, 1}, Method -> MonteCarloRule]]

Step 6

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"AdaptiveMonteCarlo", Method -> "MonteCarloRule"}]//InputForm

Output

InputForm[2.]

N integrate integration rules integration rule specification

Functions used