A

1003018704

Level: 
A
Evaluate the following integral on \( (0;\infty) \). \[ \int\left(3\sqrt x+4\sqrt[3]x-35\sqrt[4]{x^3}\right)\mathrm{d}x \]
\( 2x\sqrt x+3x\sqrt[3]x-20x\sqrt[4]{x^3}+c\text{, }c\in\mathbb{R} \)
\( \frac92 x\sqrt x+\frac{16}3 x\sqrt[3]x-\frac{245}4 x\sqrt[4]{x^3}+c\text{, }c\in\mathbb{R} \)
\( 2\sqrt x+3\sqrt[3]x-20\sqrt[4]{x^3}+c\text{, }c\in\mathbb{R} \)
\( 2\sqrt[3]x+3\sqrt[4]{x^3}-20\sqrt[7]{x^4}+c\text{, }c\in\mathbb{R} \)

1003018703

Level: 
A
Evaluate the following integral on \( \left(\frac{\pi}2;\pi\right) \). \[ \int\left(7 \cos⁡ x+\frac5{\cos^2⁡x}+\frac3{\sin^2⁡x}\right)\mathrm{d}x \]
\( 7\sin x+5\,\mathrm{tg⁡}\,x-3\,\mathrm{cotg}\,⁡x+c\text{, }c\in\mathbb{R} \)
\( -7\sin x+5\,\mathrm{tg⁡}\,x+3\,\mathrm{cotg}\,x+c\text{, }c\in\mathbb{R} \)
\( -7\sin x-5\,\mathrm{tg}\,x-3\,\mathrm{cotg}⁡\,x+c\text{, }c\in\mathbb{R} \)
\( 7\sin x-5\,\mathrm{tg}\,x+3\,\mathrm{cotg}\,⁡x+c\text{, }c\in\mathbb{R} \)

1003018702

Level: 
A
Evaluate the following integral on \( \mathbb{R} \). \[ \int\left(3^2+3x^2+3^x-\mathrm{e}^x+2^{\mathrm{e}}\right)\mathrm{d}x \]
\( 9x+x^3+\frac{3^x}{\ln⁡3} -\mathrm{e}^x+2^{\mathrm{e}} x+c\text{, }c\in\mathbb{R} \)
\( x^3+\frac{3^x}{\ln⁡3} -\mathrm{e}^x+c\text{, }c\in\mathbb{R} \)
\( 9x+3x^3+3^x-\mathrm{e}^x+\frac{2^{\mathrm{e}+1}}{\mathrm{e}+1}+c\text{, }c\in\mathbb{R} \)
\( 9x+6x+\frac{3^x}{\ln⁡3} -\mathrm{e}^x+2^\mathrm{e} x+c\text{, }c\in\mathbb{R} \)

1003018701

Level: 
A
Evaluate the following integral on \( (0;\pi) \). \[ \int\left(\pi\,\mathrm{e}^x-\frac3{\sin^2 x}\right)\mathrm{d}x \]
\( \pi\,\mathrm{e}^x+3\,\mathrm{cotg}⁡\,x+c\text{, }c\in\mathbb{R} \)
\( \pi\,\mathrm{e}^x+3\,\mathrm{tg}⁡\,x+c\text{, }c\in\mathbb{R} \)
\( \pi\,\mathrm{e}^x+\mathrm{cotg}⁡\,x+c\text{, }c\in\mathbb{R} \)
\( \pi\,\mathrm{e}^x-3\,\mathrm{cotg}⁡\,x+c\text{, }c\in\mathbb{R} \)

1003023311

Level: 
A
Which of the given degree values is not of the angle coterminal to the angle of \( 60^{\circ} \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 300^{\circ} \)
\( -300^{\circ} \)
\( -660^{\circ} \)
\( 420^{\circ} \)

1003023305

Level: 
A
Select the set that does not contain the measures of coterminal angles with an angle of radian measure \( \frac{\pi}3 \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \left\{\frac43\pi;\ -\frac{10}3\pi \right\} \)
\( \left\{\frac73\pi;\ -\frac53\pi \right\} \)
\( \left\{\frac{13}3\pi;\ \frac{61}3\pi \right\} \)
\( \left\{\frac{19}3\pi;\ \frac{25}3\pi \right\} \)

1003023304

Level: 
A
Which of the given degree values is of the angle coterminal to the angle of \( -2000^{\circ} \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 160^{\circ} \)
\(-160^{\circ} \)
\( -20^{\circ} \)
\( 200^{\circ} \)

1003023303

Level: 
A
Which value is the measure of an angle that is coterminal with an angle of radian measure \( \frac{23}3\pi \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( \frac53\pi \)
\( \frac13\pi \)
\( -\frac53\pi \)
\( -\frac43\pi \)

1003023302

Level: 
A
Select the measure of an angle that is coterminal to an angle of \( 40^{\circ} \). (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 400^{\circ} \)
\( 440^{\circ} \)
\( 360^{\circ} \)
\( 800^{\circ} \)