MCQ
$\int \sqrt{1+x^{2}} d x$ बराबर है:
  • A
    $\frac{2}{3}\left(1+x^{2}\right)^{\frac{3}{2}}+C$
  • B
    $\frac{x^{2}}{2} \sqrt{1+x^{2}}$ $+\frac{1}{2} x^{2} \log \left|x+\sqrt{1+x^{2}}\right|$
  • C
    $\frac{x}{2} \sqrt{1+x^{2}}+\frac{1}{2} \log $ $\left|x+\sqrt{1+x^{2}}\right|+C$
  • D
    $\frac{2}{3} x\left(1+x^{2}\right)^{\frac{3}{2}}+C$

Answer

माना $I=\int \sqrt{1+x^{2}} d x$
$\Rightarrow$  $I=\frac{x}{2} \sqrt{1+x^{2}}+\frac{1}{2} \log $ $\left|x+\sqrt{1+x^{2}}\right|+C$ ($\because$ $\int \sqrt{x^{2}+a^{2}} d x$ $=\frac{x}{2} \sqrt{x^{2}+a^{2}}+\frac{a^{2}}{2} $ $\log \left|x+\sqrt{x^{2}+a^{2}}\right|$)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free