{1+3x-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 : 164 of 271

Marks: +1, -0

\sqrt{1+3x-x^2}

Solution:

Let

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

=\int \sqrt{1-(x^2-3x)} dx

=\int \sqrt{1-\left(x^2-3x+\frac{9}{4}\right)+\frac{9}{4}} dx

=\int \sqrt{\left(\frac{\sqrt{13}}{2}\right)^2 - \left(x-\frac{3}{2}\right)^2} dx

=\left[ \frac{x-\frac{3}{2}}{2} \cdot \sqrt{\frac{13}{4} - \left(x-\frac{3}{2}\right)^2} + \frac{13}{8} \sin^{-1}\left(\frac{x-\frac{3}{2}}{\frac{\sqrt{13}}{2}}\right) \right] + C

=\frac{2x-3}{4} \sqrt{1+3x-x^2} + \frac{13}{8} \sin^{-1}\left(\frac{2x-3}{\sqrt{13}}\right) + C

Go to Question: