Determine el área encerrada entre las curvas \( y = x^2 \) y \( y = 4 - x^2 \), dado que se intersectan en más de dos puntos.

Determine the distance traveled by a particle moving along the curve \( y = \sin(x) \) from \( x = 0 \) to \( x = \pi \).

The area of a rectangular cross-section of a solid is given by the dimensions in terms of a linear function: width = \(x\) and height = \(3 - x\) for \(0 \leq x \leq 3\). Calculate the volume of the solid when these rectangles are stacked from \(x=0\) to \(x=3\).

\( \left. \begin{array} { l } { f ^ { \prime } ( x ) = 4 \sqrt { x ^ { 3 } } + k x ^ { - 2 } } \\ { f ^ { \prime \prime } ( x ) = } \end{array} \right. \)

If a car has an acceleration function of \( a(t) = 6t \), what is its velocity function assuming it starts from rest?

tvo: Work out Find the quadratic approximation of the function \( \sqrt{1}+x \) at \( \times \) close to 0 ?