@@ -418,33 +418,37 @@ def ff(*z):
418418class NIntegrate (Builtin ):
419419 """
420420 <dl>
421- <dt>'NIntegrate[$expr$, $interval$]'
422- <dd>evaluates the definite integral of $expr$ numerically
423- with a precision of $prec$ digits.
421+ <dt>'NIntegrate[$expr$, $interval$]'
422+ <dd>returns a numeric approximation to the definite integral of $expr$ with limits $iterval and with a precision of $prec$ digits.
423+
424+ <dt>'NIntegrate[$expr$, $interval1$, $interval2$, ...]'
425+ <dd>returns a numeric approximation to the multiple integral of $expr$ with limits $interval1$, $interval2$ and with a precision of $prec$ digits.
424426 </dl>
425427
426- >> Table[1./NIntegrate[x^k,{x,0,1},Tolerance->1*^-6], {k,0,6}]
427- : The especified method failed to return a number. Falling back into the internal evaluator.
428- = {1., 2., 3., 4., 5., 6., 7.}
429428 >> NIntegrate[Exp[-x],{x,0,Infinity},Tolerance->1*^-6]
430429 = 1.
431430 >> NIntegrate[Exp[x],{x,-Infinity, 0},Tolerance->1*^-6]
432431 = 1.
433432 >> NIntegrate[Exp[-x^2/2.],{x,-Infinity, Infinity},Tolerance->1*^-6]
434433 = 2.50663
435434
435+ >> Table[1./NIntegrate[x^k,{x,0,1},Tolerance->1*^-6], {k,0,6}]
436+ : The especified method failed to return a number. Falling back into the internal evaluator.
437+ = {1., 2., 3., 4., 5., 6., 7.}
438+
436439 >> NIntegrate[1 / z, {z, -1 - I, 1 - I, 1 + I, -1 + I, -1 - I}, Tolerance->1.*^-4]
437440 : Integration over a complex domain is not implemented yet
438441 = NIntegrate[1 / z, {z, -1 - I, 1 - I, 1 + I, -1 + I, -1 - I}, Tolerance -> 0.0001]
439442 ## = 6.2832 I
440443
441444 Integrate singularities with weak divergences:
442- >> Table[NIntegrate[x^(1./k-1.),{x,0,1.},Tolerance->1*^-6], {k,1,7.}]
445+ >> Table[ NIntegrate[x^(1./k-1.), {x,0,1.}, Tolerance->1*^-6], {k,1,7.} ]
443446 = {1., 2., 3., 4., 5., 6., 7.}
444447
445- Iterated Integral :
446- >> NIntegrate[x * y,{x, 0, 1},{y, 0, 1}]
448+ Mutiple Integrals :
449+ >> NIntegrate[x * y,{x, 0, 1}, {y, 0, 1}]
447450 = 0.25
451+
448452 """
449453
450454 messages = {
@@ -457,7 +461,7 @@ class NIntegrate(Builtin):
457461 "nlim" : "`1` = `2` is not a valid limit of integration." ,
458462 "ilim" : "Invalid integration variable or limit(s) in `1`." ,
459463 "mtdfail" : (
460- "The especified method failed to return a "
464+ "The specified method failed to return a "
461465 + "number. Falling back into the internal "
462466 + "evaluator."
463467 ),
@@ -1807,7 +1811,7 @@ class Hash(Builtin):
18071811 <dd>returns an integer hash of the specified $type$ for the given $expr$.</dd>
18081812 <dd>The types supported are "MD5", "Adler32", "CRC32", "SHA", "SHA224", "SHA256", "SHA384", and "SHA512".</dd>
18091813 <dt>'Hash[$expr$, $type$, $format$]'
1810- <dd>Returns the hash in the especified format.</dd>
1814+ <dd>Returns the hash in the specified format.</dd>
18111815 </dl>
18121816
18131817 > Hash["The Adventures of Huckleberry Finn"]
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