MCQ
If $y = \sqrt {\log x + \sqrt {\log x + \sqrt {\log x + .....\infty } } } $, then ${{dy} \over {dx}} = $
- A${x \over {2y - 1}}$
- B${x \over {2y + 1}}$
- ✓${1 \over {x(2y - 1)}}$
- D${1 \over {x(1 - 2y)}}$
$ \Rightarrow 2y\frac{{dy}}{{dx}} = \frac{1}{x} + \frac{{dy}}{{dx}} $
$\Rightarrow \frac{{dy}}{{dx}} = \frac{1}{{x(2y - 1)}}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
The general solution of the differential equation $(\text{e}^{\text{x}}+1)\text{ydy}=(\text{y}+1)\text{e}^{\text{x}}$ is:
$(\text{y}+1)=\text{k}(\text{e}^{\text{x}}+1)$
$\text{y}+1=\text{e}^{\text{x}}+1+\text{k}$
$\text{y}=\log\left\{\text{k}(\text{y}+1)(\text{e}^{\text{x}}+1)\right\}$
$\text{y}=\log\left\{\frac{\text{e}^{\text{x}}+1}{\text{y}+1}\right\}+\text{k}$
(There are two questions based on $PARAGRAPH "II"$, the question given below is one of them)
($1$) The value of $2 \int^{\frac{\pi}{2}} f(x) g(x) d x-\int^{\frac{\pi}{2}} g(x) d x$ us
($2$) The value of $\frac{16}{\pi^3} \int_0^{\frac{\pi}{2}} f(x) g(x) d x$ is
Give the answer or quetion ($1$) and ($2$)