1003027604
Level:
B
How many times is \( \int\limits_{-3}^0 \frac{x^2+x-6}{x-2}\,\mathrm{d}x \) smaller than \( \int\limits_{4}^7 \frac{5x^2-15x-20}{x+1}\,\mathrm{d}x \)?
\( 5 \) times
\( 9 \) times
they are equal
none of the options
Definite integral
1003108101
Level:
B
Evaluate the integral \( \int\limits_1^4\frac{\sqrt x-x+x^2}x\,\mathrm{d}x \).
\( 6.5 \)
\( 5.5 \)
\( 9.5 \)
\( 14.5 \)
1003108102
Level:
B
Evaluate the integral \( \int\limits_{-1}^1 \left(x^2-x\right)(x+1)\,\mathrm{d}x \).
\( 0 \)
\( \frac12 \)
\( 2 \)
\( 1 \)
1003108103
Level:
B
Evaluate the integral \( \int\limits_{-1}^1\frac{x^2+3x-10}{x-2}\,\mathrm{d}x \).
\( 10 \)
\( 6 \)
\( 8 \)
\( 12 \)
1003108104
Level:
B
Evaluate the integral \( \int\limits_{-2}^0 (x+2)^3\,\mathrm{d}x \).
\( 4 \)
\( 28 \)
\( -28 \)
\( 12 \)
1003108105
Level:
B
Evaluate the integral \( \int\limits_0^1\frac{x-1}{x+3}\,\mathrm{d}x \).
\( 1+\ln\left(\frac34\right)^4 \)
\( 1-4\ln12 \)
\( 4\ln0.75 \)
\( 4\ln12 \)
1003108107
Level:
B
Compare the value of \( \int\limits_1^2\frac{x^2\cdot\sqrt[3]x}{\sqrt[4]{x^3}}\,\mathrm{d}x \) to zero.
It is bigger than \( 0 \).
It is smaller than \( 0 \).
It equals \( 0 \).
It cannot be compared.
1003108108
Level:
B
Compare the value of \( \int\limits_1^2\frac{x^2-x}{\sqrt x}\,\mathrm{d}x \) to the number \( \frac4{15} \).
It is bigger than \( \frac4{15} \).
It is smaller than \( \frac4{15} \).
It equals \( \frac4{15} \).
It cannot be compared.
1003108201
Level:
B
Evaluate the definite integral \( \int\limits_0^{\frac{\pi}6}\frac{3\cos2t}{\cos t+\sin t}\,\mathrm{d}t \). Which of the following intervals contains the value of the integral?
\( (0.8;1.2) \)
\( (0.4;0.8) \)
\( (-0.8;-0.1) \)
\( (-0.1;0.4) \)
1003108202
Level:
B
Evaluate the definite integral \( \int\limits_{\frac{\pi}6}^{\frac{\pi}3}\frac{\mathrm{tg}\,a}{\sin2a}\,\mathrm{d}a \).
\( \frac{\sqrt3}3 \)
\( \frac{2\sqrt3}3 \)
\( -\frac{2\sqrt3}3 \)
\( -\frac{\sqrt3}3 \)