Let \( R \) be the region bounded by the following curves. Use the method of your choice to find the volume of the solid generated when \( R \) is revolved about the \( x \)-axis. \( y=4 x^{2} \) and \( y=20-x^{2} \) The volume of the solid is (Type an exact answer.)

(c) \( \int_{6}^{0}(2+5 x) e^{\frac{1}{3} x} d x \)

By using Newton-Raphson Method, determine the root for \( x^{3}+2 x^{2}-1=0 \). Given \( x_{0}=0.5 \). Give the answer correct to four decimal places. Dengan mengomenan

(b) Solve the following first order differential equations. i) \( \frac{d y}{d x}=4 x^{3}-8 x+7 \) kena tambah 1 ii) \( x \frac{d y}{d x}=5 x^{3}+4 \) iii) \( y^{3} \frac{d y}{d x}=\frac{e^{4 x}+4 x}{y} \)

Solve the following first order differential equations. \( \frac{d y}{d x}=4 x^{3}-8 x+7 \) bena tambah \( x \frac{d y}{d x}=5 x^{3}+4 \)

\( f ( x ) = \left\{ \begin{array} { l l } { \sin x } & { ; x < r } \\ { m x + b ; } & { x \geq r } \end{array} \right. \)