1.

The value of the integral I=int_(0)^(a) (x^(4))/((a^(2)+x^(2))^(4))dx is

Answer»

`(1)/(16a^(3))((pi)/(4)-(1)/(3))`
`(1)/(16a^(3))((pi)/(4)+(1)/(3))`
`(a^(3))/(16)((pi)/(4)-(1)/(3))`
`(a^(3))/(16)((pi)/(4)+(1)/(3))`

SOLUTION :Putting x=a tan `theta` in the given integral, we get
`I=(1)/(32a^(3))OVERSET(pi//4)underset(0)int(2-cos2theta-2cos2theta+cos6theta)d theta`
`rArrI=(1)/(32a^(3))[2theta-(sintheta)/(2)-(sin4theta)/(2)+(sin6theta)/(6)]_(0)^(pi//4)=(1)/(16a^(3))((pi)/(4)-(1)/(3))`


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