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 differential equation \( \frac{dy}{dx} = 3y \) and the initial condition \( y(0) = 2 \), find the particular solution.

) 8. Al sustituir \( u=\operatorname{sen} \theta \), ¿qué resultado se obtiene al evaluar \( \int \operatorname{sen}^{2} \theta \cos \theta d \theta \) ? \( \begin{array}{llll}\text { A) }-\cos ^{2} \theta \operatorname{sen} \theta+C & \text { B) } \frac{1}{6} \operatorname{sen}^{3} \theta \cos ^{2} \theta+C & \text { C) } 2 \operatorname{sen}^{2} \theta \cos ^{2} \theta-\operatorname{sen}^{3} \theta & \text { D) } \frac{1}{3}\end{array} \)

Evaluate the given improper integral or show it diverges: \[ \int_{1}^{+\infty} \frac{x^{2}}{\left(x^{3}+1\right)^{2}} d x \]

\[ f(x)=3 x^{x^{4}} \] Calcule el valor, redondeando a cuatro decimales, de \( f^{\prime}(x) \) en el punto \( x=1,07 \).

Знайдіть площу фігури, обмеженої лініями: \[ y=3 \sin x, y=-2 \sin x, x=0, x=\frac{2 \pi}{3} \]