A

9000065501

Level: 
A
Evaluate the following integral on \(\mathbb{R}\). \[ \int (x^{3} + x^{2} - 2x)\, \mathrm{d}x \]
\(\frac{1} {4}x^{4} + \frac{1} {3}x^{3} - x^{2} + c,\ c\in \mathbb{R}\)
\(\frac{1} {4}x^{4} -\frac{1} {3}x^{3} + x^{2} + c,\ c\in \mathbb{R}\)
\(3x^{2} + 2x - 2 + c,\ c\in \mathbb{R}\)
\(3x^{2} - 2x + 2 + c,\ c\in \mathbb{R}\)

9000065503

Level: 
A
Evaluate the following integral on the interval \((0;+\infty)\). \[ \int (4x^{-3} - x^{-4})\, \mathrm{d}x \]
\(- 2x^{-2} + \frac{1} {3}x^{-3} + c,\ c\in \mathbb{R}\)
\(-\frac{4} {3}x^{-2} -\frac{1} {3}x^{-3} + c,\ c\in \mathbb{R}\)
\(-\frac{3} {4}x^{-4} -\frac{1} {5}x^{-5} + c,\ c\in \mathbb{R}\)
\(- 12x^{2} + 4x^{-3} + c,\ c\in \mathbb{R}\)

9000065610

Level: 
A
Using definite integral find the area of the triangle defined by the following three inequalities \[ \begin{aligned}y& > 0, & \\y& < x + 3, \\y& < 3 - x. \\ \end{aligned} \]
\(\int _{-3}^{0}(x + 3)\, \mathrm{d}x +\int _{ 0}^{3}(3 - x)\, \mathrm{d}x\)
\(\int _{0}^{3}(x + 3)\, \mathrm{d}x\)
\(\int _{-3}^{3}(3 - x)\, \mathrm{d}x\)
\(\int _{-3}^{0}(3 - x)\, \mathrm{d}x +\int _{ 0}^{3}(x + 3)\, \mathrm{d}x\)