Consider the function \( f(x) = x^2 \). Use the Fundamental Theorem of Calculus to compute the definite integral from 1 to 3.

\( \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 2 x } f ( x , y ) d y d x \)

8.- Obtener el Volumen encerrado por las superficies: \( x^{2}+y^{2}=4 ; x+z=2 \); \( y=4 ; x=0 ; z=0 \) (Primer octante).

A function \( f \) is defined as \( f(x)=\frac{5}{(x+2)^{2}}-\frac{2}{x+2} \) for \( x>0 \). Find an expression for \( f^{\prime}(x) \) and determine whether \( f \) is an increasing function, a decreasing function or aeither.

Найдите неопределенный интеграл: \( \, \int (3x^2 + 2x - 1) \, dx \)

\( z \int _ { 0 } ^ { + \infty } t ^ { z } e ^ { - t } d t \)