The diagram shows the region $M$, which is bounded by the curve $y = 2x^{2}$, the line \(y = x +

Question

The diagram shows the region $M$, which is bounded by the curve $y = 2x^{2}$, the line $y = x + 1$ and the $y$-axis and the region $K$, which is bounded by $y = 2x^{2}$, the $x$-axis, and the line $x = 1$. Find the volume of solid formed exactly when $K$ is rotated through $4$ right angles about the $x$-axis. Find the volume of solid formed exactly when $M$ is rotated through $2\pi$ about the $y$-axis. Find the volume of solid formed when $M$ is rotated through $2\pi$ about the $x$-axis.

Accepted Answer

(i) $\frac{4\pi}{5}\text{ units}^3$ (ii) $\frac{2\pi}{3}\text{ units}^3$ (iii) $\frac{23\pi}{15}\text{ units}^3$

Applications of Integration - Volume of Revolution

Applications of Integration - Volume of Revolution

Video Solution:

Solution:

Solution locked