What is the arc length of the parametrically defined curve given by \( x(t) = t, y(t) = t^3 \) for \( t \) in the interval \([0, 2]\)?

\( \left. \begin{array} { l } { \frac { \partial ^ { 5 } } { \partial x ^ { 3 } \partial y ^ { 2 } } ( x ^ { 2 } y ^ { 3 } e ^ { x y } ) } \\ { \frac { \partial ^ { 4 } } { \partial x ^ { 2 } \partial z ^ { 2 } } ( x ^ { 3 } z ^ { 4 } \sin ( x z ) ) } \end{array} \right. \)

Evaluate the derivative \( y=\sinh (x) \)

7. \( \frac{d}{d x}\left(x^{3}-3 x^{2}+2 x\right) \)

8. \( \int_{0}^{1}(2 x+3) d x \)

\( \int _ { 0 } ^ { x } y ( t ) d t = x _ { + } ^ { 3 } \int _ { 0 } ^ { x } \sin ( x , t ) y ( t ) d t \)