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  • Integrate the functions in Exercises 1 to 9. root of 1 - 4x - x^2

Integrate the functions in Exercises 1 to 9.

    Q5.    \sqrt{1-4x-x^2}

Answers (1)

best_answer

Given function \sqrt{1-4x-x^2},

So, let us consider the function to be;

I = \int\sqrt{1-4x-x^2}dx

 = \int\sqrt{1-(x^2+4x+4-4)}dx = \int\sqrt{1+4 -(x+2)^2}dx

= \int\sqrt{(\sqrt5)^2 -(x+2)^2}dx

And we know that, \int \sqrt{a^2-x^2}dx = \frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}+C

\therefore I = \frac{x+2}{2}\sqrt{1-4x-x^2}+\frac{5}{2}\sin^{-1}\left ( \frac{x+2}{\sqrt5} \right )+C

 

Posted by

Divya Prakash Singh

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