Home
Class 12
MATHS
Evaluate int(dx)/(sqrt(1-x^(2))(1+sqrt(1...

Evaluate `int(dx)/(sqrt(1-x^(2))(1+sqrt(1-x^(2))))`.

Text Solution

Verified by Experts

Put `x="sin"theta`
` :. dx="cos"theta"d"theta`
` :. I=int(dx)/(sqrt(1-x^(2))(1+sqrt(1-x^(2))))`
`=int("cos"theta"d"theta)/("cos"theta(1+"cos"theta))`
`=(1)/(2)int"sec"^(2)(theta)/(2)"d"theta`
`="tan"(theta)/(2)+c`
`=(2"sin"(theta)/(2)"cos"(theta)/(2))/(2"cos"^(2)(theta)/(2))+c`
`=("sin"theta)/(1+"cos"theta)+c`
`=(x)/(1+sqrt(1-x^(2)))+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXAMPLE|18 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int (dx)/(sqrt(1-x-x^(2)))

Evaluate: int(x^2)/(sqrt(1-x))dx

Evaluate: int(dx)/(x^3sqrt(x^2-1))

Evaluate: int(x^2)/(sqrt(1-x^6))dx

Evaluate int(dx)/((1+x^(2))sqrt(1-x^(2))).

Evaluate int(dx)/(x^(2)sqrt(1+x^(2))) .

Evaluate: int (x dx)/sqrt(3x^2+1)

Evaluate: int(x^3)/(sqrt(x^2+1))dx

Evaluate: int_0^(1)x(dx)/(sqrt(1-x^(2)))

int(dx)/((1-x^(2))sqrt(1-x^(2)))