CBSE Class 12-science Answered
please solve it
Asked by www1028 | 12 Sep, 2010, 10:08: PM
Expert Answer
∫dx/(2x - x2)3/2 =
∫dx/(1 - 1 + 2x - x2)3/2 =
∫dx/(1 - (x - 1)2 )3/2 =
∫dx/[(1 - (x - 1))(1 + (x - 1))]3/2 =
∫dx/[(2 - x )x]3/2 =
∫dx/[(2 - x )3/2x3/2] =
Using partial fractions,
1/[(2 - x )3/2x3/2] = A/x3/2 + B/(2 - x )3/2
Hence we find,
A = 1/23/2 = B
∫dx/[(2 - x )3/2x3/2] =
(1/23/2)∫dx/(2 - x )3/2 + dx/x3/2] =
(1/23/2){2/(2 - x )1/2 - 2/x1/2] + C =
{1/(2(2 - x ))1/2 - 1/(2x)1/2] + C
regards,
Team,
TopperLearning.
Answered by | 13 Sep, 2010, 09:55: PM
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