Find the area between the curves. \( y=x^{2}-43, y=5-2 x \) The area between the curves is (Type an integer or decimal rounded to the nearest tenth as needed.)

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

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

(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) \( y^{3} \frac{d y}{d x}=\frac{e^{4 x}+4 x}{y} \)

integral \( \int_{0}^{1} \int_{e^{y}}^{e} \frac{x}{\ln x} d x d y \) (by

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