7) Calcular el volumen del elipsoide de revolución dado por las ecuaciones paramétricas \[ x=a \cdot \cos t, \quad y=b \cdot \operatorname{sent} \] (elipse de semiejes \( a \) y \( b \) al girar alrededor del eje mayor \( (a>b) \)

Evaluate the following definite integral using the Fundamental Theorem of Calculus. \( \frac{1}{7} \int_{0}^{\ln 4} e^{x} d x \)

Find the following limit or state that it does not exist \[ \lim _{x \rightarrow-1} \frac{4(2 x-2)^{2}-64}{x+1} \]

Find the point(s) at which the function \( f(x)=10-|x| \) equals its average value on the interval \( [-10,10] \) The function equals its average value at \( x=\square \) (Type an integer or a fraction. Use a comma to separate answers as needed.)

Given the following velocity function of an object moving along a line, find the position function with the given initial position.

\( \int _ { - 1 } ^ { 1 } \frac { x \cos ^ { 2 } x } { 1 + x ^ { 2 } } d x \)