Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

Find ∫√x/√(a^3−x^3)dx - Mathematics and Statistics

Find `intsqrtx/sqrt(a^3-x^3)dx`

Advertisement Remove all ads

Solution

`I=intsqrtx/sqrt(a^3-x^3)dx`

Let`x^(3/2)=t`

`=>3/2x^(1/2)dx=dt`

`x^(1/2)dx=2/3dt`

Putting the values in I, we get 

`I=intsqrtx/sqrt(a^3-x^3)dx`

`=2/3int1/(sqrt(a^3-t^2))dt`

Using the following formula of integration, we get

`intdx/sqrt(a^2-x^2)=sin^(-1)(x/a)`

`:.2/3int1/sqrt(a^3-t^2)dt=2/3sin^(-1)(t/(a^(3/2)))+C`

Again, putting the value of t, we get

`2/3int1/sqrt(a^3-t^2)dt=2/3sin^(-1)(t/a^(3/2))+C`

`=2/3sin^(-1)(x^(3/2)/a^(3/2))+C`

Here, C is constant of integration.

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×