{x}{{x+4}}, x > 0 - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 33 of 271

Marks: +1, -0

\frac{x}{\sqrt{x+4}}, x > 0

Solution:

Let

I=\int \frac{x}{\sqrt{x+4}} dx

Put

x + 4 = t

\Rightarrow dx = dt

. Also

x = t - 4

\therefore I = \int \frac{t-4}{t} dt

= \int (t^{1/2} - 4 t^{-1/2}) dt

= \frac{2}{3} t^{3/2} - 4 \times 2 t^{1/2} + C

= \frac{2}{3} (x+4)^{3/2} - 8 (x+4)^{1/2} + C

= \frac{2}{3} (x+4)^{1/2} \left[ x+4-12 \right] + C

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

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