Intg dx/(sqrt(7-3x-x^2))

Asked by Anuradha Pradeep | 6th Nov, 2012, 11:04: AM

Expert Answer:

7 - 3x - x2 = 7 - (x2 + 3x + 9/4 - 9/4)
                = 7 + 9/4 - (x + 3/2)2
                = 37/4 - (x + 3/2)2
 
Thus, we have:
Integral dx/(sqrt(7-3x-x^2))
= Integral dx/sqrt(37/4 - (x + 3/2)2)
Put x + 3/2 = t, so dx = dt
 
Integral dx/sqrt(37/4 - (x + 3/2)2) = Integral dt/sqrt(37/4 - (t)2)
This integral can now easily be evaluated.

Answered by  | 6th Nov, 2012, 07:51: PM

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