Home
Class 12
MATHS
Evaluate: int(dx)/((x-p)sqrt((x-p)(x-q))...

Evaluate: `int(dx)/((x-p)sqrt((x-p)(x-q)))`

Text Solution

Verified by Experts

The correct Answer is:
`-(2)/(p-q)sqrt((x-q)/(x-p))+C`
`sqrt((x-q)/(x-p))=t`
` :. (1)/(2)((x-p)/(x-q))^(1//2)((x-p)1-(x-q)1)/((x-p)^(2))dx=dt.`
`or (1)/(2)(q-p)/(sqrt(x-q)(x-p)^(3//2))dx=dt`
`or (dx)/((x-p)^(3//2)sqrt((x-q)))=(2dt)/(q-p)`
`or I=-int(2dt)/(p-q)t= -(2)/(p-q)sqrt((x-q)/(x-p))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.3|16 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(P+Q)dx

Evaluate int(dx)/(x+sqrt(x))

Evaluate: int(x)/(sqrt(x+2))dx

Evaluate: int(x)/(sqrt(x+a)+sqrt(x+b))dx

Evaluate; int(x)/(1+sqrt(x))dx

Evaluate: int(1)/(sqrt(x)+x)dx

Evaluate int(x)/(sqrt(x+4))dx

Evaluate: int_(-a)^(a)sqrt((a-x)/(a+x))dx

(a) Evaluate: int(x)/(1+sqrt(x))dx

Evaluate: int(sqrt(x)dx)/(1+x)