Find the area between the curves. \[ x=-2, x=2, y=3 e^{3 x}, y=2 e^{3 x}+1 \] The area between the curves is approximately (Do not round until the final answer. Then round to the nearest hundredth as needed.)

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

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

اجد التكامل غير المحدود للدالة \( f(x) = 3x^2 \).

Calcule \( \int \frac{x^{4} - 5x^{2} + 6}{x-2} \,dx \) aplicando o método de divisão longa.

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