9000150302
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int 8\sin x\, \text{d}x
\]
\(- 8\cos x + c,\ c\in \mathbb{R}\)
\(8\cos x + c,\ c\in \mathbb{R}\)
\(8\sin x + c,\ c\in \mathbb{R}\)
\(- 8\sin x + c,\ c\in \mathbb{R}\)
A
9000150303
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int 9\mathrm{e}^{x}\, \text{d}x
\]
\(9\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)
\(9 -\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)
\(9 +\mathrm{e} ^{x} + c,\ c\in \mathbb{R}\)
\(- 9\mathrm{e}^{x} + c,\ c\in \mathbb{R}\)
9000150304
Level:
A
Evaluate the following integral on the interval \((0;+\infty)\).
\[
\int \frac{5}
{x}\, \text{d}x
\]
\(5\ln |x| + c,\ c\in \mathbb{R}\)
\(5x^{2} + c,\ c\in \mathbb{R}\)
\(\frac{\ln |x|}
{5} + c,\ c\in \mathbb{R}\)
\(\frac{5}
{x^{2}} + c,\ c\in \mathbb{R}\)
9000150305
Level:
A
Evaluate the following integral on the interval \(\left(0;\frac{\pi}2\right)\).
\[
\int \frac{8}
{\cos ^{2}x}\, \text{d}x
\]
\(8\mathop{\mathrm{tg}}\nolimits x + c,\ c\in \mathbb{R}\)
\(- 8\mathop{\mathrm{cotg}}\nolimits x + c,\ c\in \mathbb{R}\)
\(8\mathop{\mathrm{cotg}}\nolimits x + c,\ c\in \mathbb{R}\)
\(- 8\mathop{\mathrm{tg}}\nolimits x + c,\ c\in \mathbb{R}\)
9000150306
Level:
A
Evaluate the following integral on the interval \((0;+\infty)\).
\[
\int \frac{9}
{x^{5}}\, \text{d}x
\]
\(- \frac{9}
{4x^{4}} + c,\ c\in \mathbb{R}\)
\(\frac{9}
{x^{6}} + c,\ c\in \mathbb{R}\)
\(- \frac{3}
{2x^{6}} + c,\ c\in \mathbb{R}\)
\(\frac{9}
{x^{4}} + c,\ c\in \mathbb{R}\)
9000150307
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int 8\cdot 5^{x}\, \text{d}x
\]
\(\frac{8\cdot 5^{x}}
{\ln 5} + c,\ c\in \mathbb{R}\)
\(\frac{8\cdot 5^{x}}
{\ln x} + c,\ c\in \mathbb{R}\)
\(8\cdot 5^{x}\cdot \ln 5 + c,\ c\in \mathbb{R}\)
\(8\cdot 5^{x}\cdot \ln x + c,\ c\in \mathbb{R}\)
9000150308
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int \frac{\cos x}
{8}\, \text{d}x
\]
\(\frac{\sin x}
{8} + c,\ c\in \mathbb{R}\)
\(-\frac{\sin x}
{8} + c,\ c\in \mathbb{R}\)
\(\sin x + c,\ c\in \mathbb{R}\)
\(-\sin x + c,\ c\in \mathbb{R}\)
9000148906
Level:
A
Each candidate in a tender is fluent in at least one out
of two required languages (English and French). There are
\(20\) candidates fluent
in English and \(14\)
candidates fluent in French. From these amounts
\(10\)
candidates are fluent in both languages. How many candidates are there in the
tender?
\(24\)
\(34\)
\(14\)
\(44\)
9000146706
Level:
A
Expand the following polynomial.
\[
(2x + 3)^{2} - (2 - x)^{2}
\]
\(3x^{2} + 16x + 5\)
\(3x^{2} + 8x + 13\)
\(3x^{2} + 13\)
\(3x^{2} + 5\)
9000150101
Level:
A
Evaluate the following integral on \(\mathbb{R}\).
\[
\int \left (\cos x -\sin x\right )\, \mathrm{d}x
\]
\(\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(\sin x -\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x +\cos x + c,\ c\in \mathbb{R}\)
\(-\sin x -\cos x + c,\ c\in \mathbb{R}\)