C

9000066009

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

9000066010

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

9000066007

Level: 
C
Evaluate the following integral on the interval \((0;+\infty)\). \[ \int x^{2}\ln x\, \mathrm{d}x \]
\(\frac{1} {3}x^{3}\ln x -\frac{1} {9}x^{3} + c,\ c\in \mathbb{R}\)
\(\frac{1} {2}x^{2}\ln x -\frac{1} {4}x^{2} + c,\ c\in \mathbb{R}\)
\(x\ln x -\frac{1} {2}x^{2} + c,\ c\in \mathbb{R}\)
\(x\ln x - x + c,\ c\in \mathbb{R}\)

9000064801

Level: 
C
The sides of a right triangle form three consecutive terms of an arithmetic sequence. The perimeter of the triangle is \(60\, \mathrm{cm}\). Find the hypotenuse of the triangle (the longest side).
\(25\, \mathrm{cm}\)
\(12\, \mathrm{cm}\)
\(15\, \mathrm{cm}\)
\(20\, \mathrm{cm}\)
\(30\, \mathrm{cm}\)

9000064805

Level: 
C
The sides of a box form three consecutive terms of an arithmetic sequence. The volume of the box is \(665\, \mathrm{cm}^{3}\). The shortest side is \(5\, \mathrm{cm}\). Find the surface area of the box.
\(501\, \mathrm{cm}^{2}\)
\(315\, \mathrm{cm}^{2}\)
\(615\, \mathrm{cm}^{2}\)
\(805\, \mathrm{cm}^{2}\)
\(1\: 215\, \mathrm{cm}^{2}\)