Home
Class 12
MATHS
int (0)^(1) (x)/(x^(2)+1)dx...

`int _(0)^(1) (x)/(x^(2)+1)dx`

Text Solution

Verified by Experts

`"Let "I= int_(0)^(1)(x)/(x^(2)+1)dx`
`"Let " x^(2)+1=t rArr xdx=(dt)/(2)`
`x=0 rArr t=1`
`" and " x=1 rArr t=2`
`:. I= int_(1)^(2) (1)/(t).(dt)/(2) =(1)/(2) int_(1)^(2) (1)/(t)dt =(1)/(2) [log |t|]_(1)^(2)`
`=(1)/(2)[log |2|-log |1|]=(1)/(2)log 2.`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.11|21 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|44 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.9|22 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(1)(x+1)/(x^(2)+1)dx

int_(0)^(1)(x-1)/(x^(2)-1)dx

int_(0)^(1) (1)/(x^(2)+x+1)dx

Evaluate: int_(0)^(4)(1)/(x+sqrt(x))dx( ii) int_(0)^(1)(2x)/(5x^(2)+1)dx

Evaluate: int_(0)^(1)(2x)/(5x^(2)+1)dx

int_(0)^(1) x^(2)/(x^(2)+1)dx=

int_(0)^(1)(2x)/((1+x^(2)))dx

Evaluate the following definite integral: int_(0)^(1)(1)/(2x^(2)+x+1)dx

int_(0)^(1) (x^(2))/(1+x^(2))dx is equal to

The value of int_(0)^(1)(x^(2))/(1+x^(2))dx is