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The value of \int \frac{d(sinx)}{\sqrt{1-sin^{2}}x} is equal to

  • Option 1)

    x+c

  • Option 2)

    3x+c

  • Option 3)

    x^{2}+c

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt

Integration by substitution -

The functions when on substitution of the variable of integration to some quantity gives any one of standard formulas.

 

 

- wherein

Since \int f(x)dx=\int f(t)dt=\int f(\theta )d\theta all variables must be converted into single variable ,\left ( t\, or\ \theta \right )

 

 

 

Let \sin x =z  Þ    d\left ( \sin x \right )=dz

                        \int \frac{dz}{\sqrt{1-z^{2}}}=\sin^{-1}z+c=\sin^{-1}\left (\sin x \right )+c=x+c 


Option 1)

x+c

Option 2)

3x+c

Option 3)

x^{2}+c

Option 4)

none of these

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Plabita

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