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) $(-1,\frac15)$, $(1,\frac15)$. (ii) $\tan^{-1}2-\frac2{15}$ units$^2$. (iii) $\frac{\pi}{4}\ln5-\frac{\pi}{10}$ units$^3$.

2025 MI P1 Q10

2025 MI P1 Q10

Solution:

Solution locked