Home
Class 12
MATHS
Evaluate : int(0)^(a) (dx)/(x^(2) +a^(2)...

Evaluate : `int_(0)^(a) (dx)/(x^(2) +a^(2)) `

Text Solution

Verified by Experts

`int_(0)^(a) (1)/(x^(2) +a^(2))dx`
` =(1)/(a) [ tan ^(-1) .(x)/(a)]_(0)^(a)`
` =1/a [tan ^(-1). (a)/(a) -tan ^(-1) 0]`
` =1/a[tan^(-1) 1-0]=(pi)/(4a) .`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7a|14 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7b|26 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

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

Evaluate int_(0)^(2)2^(x)dx

Evaluate int_(0)^(2)e^(x)dx

Evaluate : int_(0)^(4) (dx)/(sqrt(x^(2) +2x +3))

Evaluate: int_(0)^(3) x^(2) dx

Evaluate : int_(0)^(a) (1)/(sqrt(a^(2) -x^(2))) dx

Evaluate : int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))

Evaluate: int_(0)^(a)(dx)/(x+sqrt((a^(2)-x^(2))))quad or int_(0)^((pi)/(2))(d theta)/(1+tan theta)

Evaluate int_(0)^(5)|x-2|dx

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