Sir, Plz solve this Definite Integral
Asked by
| 26th Jan, 2010,
12:15: PM
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,
11:04: AM
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