{1-4x-x² - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.7
Integrate the functions in Exercises 158 to 166.

Question : 162 of 271

Marks: +1, -0

\sqrt{1-4x-x^2}

Solution:

Let

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

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

=\int\limits\sqrt{5-(x+2)^2}dx

=\int\limits\sqrt{(\sqrt{5})^2-(x+2)^2}dx

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

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

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