Plz solve this sum

Asked by  | 5th Feb, 2010, 04:57: AM

Expert Answer:

Put x = tan-1(2t/(1-t2)) or tanx = 2t/(1-t2)

then dx = 2 dt/(1+t2) and x = 0, t = 0; x = π/2, t = ±1

and sinx = 2t/(1+t2) and cosx = (1-t2)/(1+t2)

2cosx + 4sinx = 2((1-t2)/(1+t2) + 4(2t/(1+t2)) = [2(1-t2) + 8t]/(1+t2) = 2[(1-t2) + 4t]/(1+t2)

dx/(2cosx + 4sinx) = dt/{(1+t2)[(1-t2) + 4t]/(1+t2)} = dt/[(1-t2) + 4t] = dt/[5 - (t-2)2]

This can further be solved by partial fraction or using standard integral, and subsequent use of limits will complete the proof.

Regards,

Team,

TopperLearning.

Answered by  | 5th Feb, 2010, 11:03: AM

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