Question
Question: If I = \(\int_{}^{}\frac{dx}{\sqrt{(x - \alpha)(\beta - x)}}\). (b \<a) then value of I is:...
If I = ∫(x−α)(β−x)dx. (b <a) then value of I is:
A
sin–1(β−α2x−α−β)+ C
B
sin–1(β−αx−α−β)
C
sin– (α+β2x+β−α)
D
None of these
Answer
sin–1(β−α2x−α−β)+ C
Explanation
Solution
Put t = 21 (x – a + x – b)
= x – 21 (a + b), so that
(x – a) (b – x) =[β−21(α+β)−t]
= 41 (b – a)2 – t2
\ I = sin–1 (β−α2t)+ C = sin–1 (β−α2x−α−β)+ C