JEE PYQ: Area Under Curves Question 5
Question 5 - 2021 (18 Mar Shift 2)
Let $y = y(x)$ be the solution of the differential equation $xdy - ydx = \sqrt{(x^2 - y^2)}dx$, $x \geq 1$, with $y(1) = 0$. If the area bounded by the line $x = 1$, $x = e^\pi$, $y = 0$ and $y = y(x)$ is $\alpha e^{2\pi} + \beta$, then the value of $10(\alpha + \beta)$ is equal to ____.
Type: Numerical
Show Answer
Answer: 4
Solution
$y = x\sin(\ln x)$. $A = \int_1^{e^\pi} x\sin(\ln x),dx = \frac{e^{2\pi}+1}{5}$. So $\alpha = \frac{1}{5}$, $\beta = \frac{1}{5}$, $10(\alpha+\beta) = 4$.
BETA
