Khan Academy 0 Aproxima el área entre el eje \( x \) y \( f(x)=(x-3)^{2} \) de \( x=0 \) a \( x=6 \) mediante una suma de Riemann central con 3 subdivisiones iguales. El área aproximada es \( \square \)

Calcular la derivada de las a) \( F_{(x)}=\left(x^{5} \cdot \operatorname{sen} x\right) \)

\( y ^ { \prime \prime \prime } + y = e ^ { x } + e ^ { - x } \cos ( 3 x ) + x ^ { 3 } \)

Question 3 finding a potential for it. (a) Find the volume of the parallelopiped whose coterminus edges are given by the vectors \( \left.\vec{A}=2 \vec{i}-e^{x} \cos y+y z\right) \vec{i}+\left(x z-e^{x} \sin y\right) \vec{j}+(x y+z) \vec{k} \) is conservative by \( 3 \vec{j}+4 \vec{k}, \vec{B}=\vec{i}+2 \vec{j}-\vec{k} \) and \( \vec{C}=3 \vec{i}-\vec{j}+2 \vec{k} \).

Encuentre \( y^{\prime} \) si \( y^{5}+3 y^{2}-2 x^{4}=-4 \)

(f) Find the constants \( a, b, c \), so that \[ \vec{F}=(x+2 y+a z) \vec{i}+(b x-3 y-z) \vec{j}+(4 x+c y+2 z) \vec{k} \] is irrotational and hence find function \( \phi \) such that \( \vec{F}=\nabla \phi \). (g) Show that the vector field \( \vec{F}=\left(e^{x} \cos y+y z\right) \vec{i}+\left(x z-e^{x} \sin y\right) \vec{j}+(x y+z) \vec{k} \) is conservative by (3 marks) finding a potential for it.