CBSE Class 12-science Answered
1.How will u integrate x^2/sqrt(1-x^2)
2. Integrate x/sqrt(1-x^2)
Asked by GeoffreyRichards | 19 Oct, 2010, 04:54: PM
Expert Answer
Dear Student,
To evaluate, ∫x2 dx/√(1 - x2)
Put x = sinθ
dx = cosθ dθ
∫x2 dx/√(1 - x2) = ∫sin2θ cosθdθ/√(1 - sin2θ)
= ∫sin2θ cosθdθ/cosθ
= ∫sin2θ dθ
= ∫(1 - cos2θ)dθ / 2 .. using cos2θ = 1 - 2sin2θ
= (θ - sin2θ /2)/2 + c
= (θ/2 - sin2θ /4 + c
= (sin-1x)/2 - (sin2(sin-1x))/4 + c ... Answer Q1
Similarly the second becomes after same substitution,
∫x dx/√(1 - x2) = ∫sinθ dθ
= - cosθ + c
= - cos sin-1 x + c .. Answer Q 2
regards,
Team,
TopperLearning.
Answered by | 19 Oct, 2010, 09:59: PM
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