Question
Question: If b \> a, and I = \(\int_{a}^{b}\sqrt{\frac{x - a}{b - x}}\)dx, then I equals...
If b > a, and I = ∫abb−xx−adx, then I equals
A
2π (b – a)
B
p (b – a)
C
p/2
D
2p (b – a)
Answer
2π (b – a)
Explanation
Solution
Put b –x = t2, so that
I = ∫b−a0t2b−t2−a (–2t) dt
= 2∫0cc2−t2dt where c = b−a
= 2 [21tc2+t2+2c2sin−1(ct)]0c
= 0 + c2 sin–1 (1) – 0
= 2π (b –a)