The curves $C_1$ and $C_2$ are given by the equations $y = \frac{1}{1 + 4x^2}$ and \(y = \frac

Question

The curves $C_1$ and $C_2$ are given by the equations $y = \frac{1}{1 + 4x^2}$ and $y = \frac{x^2}{5}$ respectively. Find the coordinates of the intersection points for $C_1$ and $C_2$.[2] The region $R$ is bounded by $C_1$ and $C_2$. Find the exact area of $R$.[5] Find the exact volume generated when $R$ is rotated through $\pi$ radians about the $y$-axis.[5]

Accepted Answer

(i)coordinates of intersection points are (-1,$\frac{1}{5}$),(1,$\frac{1}{5}$) (ii)$\tan^{-1}(2)-\frac{2}{15}$units$^2$ (iii)$\frac{\pi}{4}\ln 5-\frac{\pi}{10}$units$^3$

2025 MI P1 Q10

2025 MI P1 Q10