InterviewSolution
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InterviewSolution
| 1. |
1+x2-I-x21+x2+1-x2dx |
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Answer» y= tan –1[{√(1 + x^2) – √(1 – x^2)}/{√(1 + x^2) + √(1 – x2)}]Put x^2= cos θ, theny = tan –1[{√(1 + cos θ) – √(1 – cos θ)}/{√(1 + cos θ) + √(1 – cos θ)}]= tan-1[(√2 cos θ/2 – √2 sin θ/2)/(√2 cos θ/2 + √2 sin θ/2)]= tan-1[(1 – tan θ/2)/(1 + tan θ/2)]= tan-1[tan(π/4 – θ/2)]= π/4 – θ/2 = π/4 – 1/2 cos –1 x^2.Differentiating w.r.t. x we getdy/dx = 0 – 1/2. d/dx(cos-1x^2)= – 1/2. – 1/√{1 – (x2)2}.d/dx(x^2)= 1/2 .1/√(1 – x^4). 2x= x/√(1 – x^4) thnxx |
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