1003027701
Level:
A
How much bigger is \( \int\limits_0^{\pi}(x+\sin x)\,\mathrm{d}x \) than \( \int\limits_1^{\pi}x\,\mathrm{d}x \)?
\( \frac52 \)
\( 0.5 \)
\( \pi-1 \)
\( \frac32 \)
Definite integral
1003027702
Level:
A
How much smaller is \( \int\limits_{-\frac{\pi}2}^{\frac{\pi}2}\sin x\,\mathrm{d}x \) than \( \int\limits_{0}^{\pi}(\cos x + 1)\,\mathrm{d}x \)?
\( \pi \)
\( 1-\pi \)
\( \pi-1 \)
\( 2\pi \)
1003027703
Level:
A
Compare two definite integrals \( I_1=\int\limits_0^{\frac{\pi}2}\cos x\,\mathrm{d}x \) and \( I_2=\int\limits_0^{2\pi}2\cos x\,\mathrm{d}x \).
\( I_1 \) is bigger than \( I_2 \) by \( 1 \).
\( I_1 \) is smaller than \( I_2 \) by \( 1 \).
\( I_1 \) is equal to \( I_2 \).
\( I_1 \) is smaller than \( I_2 \) by \( 2 \).
1003027704
Level:
A
Compare two definite integrals \( I_1=\int\limits_{-1}^1x^8\,\mathrm{d}x \) and \( I_2=\int\limits_{-1}^1x^2\,\mathrm{d}x \).
\( I_2 \) is bigger than \( I_1 \) by \( \frac49 \).
\( I_1 \) is bigger than \( I_2 \) by \( \frac49 \).
\( I_2 \) is bigger than \( I_1 \) by \( \frac29 \).
\( I_1 \) is bigger than \( I_2 \) by \( \frac29 \).
1003027705
Level:
A
How much smaller is \( \int\limits_0^{1} x^{15}\,\mathrm{d}x \) than \( \int\limits_0^{1} x^{5}\,\mathrm{d}x \)?
\( \frac5{48} \)
\( \frac{11}{48} \)
\( \frac5{32} \)
\( \frac{11}{32} \)
1003027706
Level:
A
How much smaller is \( \int\limits_{\frac{5\pi}6}^{\pi}3\sin x\,\mathrm{d}x \) than \( \int\limits_0^{\frac{5\pi}6}3\sin x\,\mathrm{d}x \)?
\( 3\sqrt3 \)
\( 3\sqrt2 \)
6
\( \frac{\pi}6 \)
1003027707
Level:
A
Which of the given values of \( a \) makes the statement true?
\[ \int\limits_0^51.6x\,\mathrm{d}x-a = \int\limits_0^50.6x\,\mathrm{d}x \]
\( a=12.5 \)
\( a=1 \)
\( a=13.5 \)
\( a=8 \)
1003027708
Level:
A
How many times bigger is \( \int\limits_{5}^{10}(1.2x-6)\,\mathrm{d}x \) than \( \int\limits_{0}^{5}0.4x\,\mathrm{d}x \)?
\( 3 \) times
\( 2 \) times
\( 4 \) times
\( 7 \) times
1003027709
Level:
A
How many times bigger is \( \int\limits_0^7\left(-\frac47x+4\right)\,\mathrm{d}x \) than \( \int\limits_{-1}^0\left(-\frac43x+\frac43\right)\,\mathrm{d}x \)?
\( 7 \) times
\( 6 \) times
\( 14 \) times
\( 2 \) times
1003027710
Level:
A
How many times bigger is \( \int\limits_0^4 (3x+3)\,\mathrm{d}x \) than \( \int\limits_2^3 (3x-6)\,\mathrm{d}x \)?
\( 24 \) times
\( 6 \) times
\( 9 \) times
\( 54 \) times