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If bgta, then int(a)^(b)(dx)/(sqrt((x-a)...

If `bgta,` then `int_(a)^(b)(dx)/(sqrt((x-a)(b-x)))` is equal to

A

`(pi)/(2)`

B

`pi`

C

`(pi)/(2)(b-a)`

D

`(pi)/(4)(b-a)`

Text Solution

Verified by Experts

The correct Answer is:
B
`int _(a)^(b) (dx)/(sqrt(x-a)(b-x))=int_(a)^(b) 1/(sqrt(-x^(2) + (a+b) x - ab))dx` ,
` = int _(a)^(b) 1/(sqrt(((b-a)/2)^(2) - (x-(a+b)/2)^(2)))dx = [ sin^(-1).(((x-(a+b))/2)/((b-2)/2))]_(a)^(b)`
` = sin^(-1) 1- sin^(-1) (-1)`
` = pi/2 + pi/2 = pi`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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