Sum

Given `int_0^x 1/(x^2+a^2) dx=1/atan^(-1)(x/a)`using DUIS find the value of `int_0^x 1/(x^2+a^2) `

Advertisement Remove all ads

#### Solution

`int_0^x 1/(x^2+a^2) dx=1/atan^(-1)(x/a)`

Differentiate w.r.t a , taking ‘a’ as parameter

`d/(da)int_0^x 1/(x^2+a^2) dx=d/(da)[1/atan^(-1)(x/a)]`

Applying D.U.I.S rule,

D.U.I.S rule says that if function and its partial derivative is continuous then we can apply differential operator in the integral operator by converting it into partial derivative taking one parameter fro function.

`int_0^xdel/(dela) 1/(x^2+a^2) dx=-1/atan^(-1)(x/a)xx1/a+(-x)/(a(x^2+a^2)`

`int_0^x(2a^2)/(x^2+a^2) dx=-1/atan^(-1)(x/a)xx1/a+(-x)/(a(x^2+a^2)`

`int_0^x(dx)/(x^2+a^2)^2 dx=-1/(2a^3)tan^(-1) x/a+x/(2a^2(x^2+a^2)`

Concept: Method of Variation of Parameters

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads