{1+x²/9} - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 166 of 271

Marks: +1, -0

\sqrt{1+\frac{x^2}{9}}

Solution:

Let

I=\int\sqrt{1+\frac{x^2}{9}}dx

=\frac{1}{3}\int\sqrt{x^2+3^2}dx

=\frac{1}{3}\left[\frac{x}{2}\sqrt{x^2+9}+\frac{9}{2}\log\left|x+\sqrt{x^2+9}\right|\right]+C

=\frac{x}{6}\sqrt{x^2+9}+\frac{3}{2}\log\left|x+\sqrt{x^2+9}\right|+C

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