1003027714
Level:
A
Which of the given values of \( a \) makes the statement true?
\[ \int\limits_0^1x^8\,\mathrm{d}x = a\cdot\int\limits_{-1}^0x^{24}\,\mathrm{d}x\]
\( a=2.\overline{7} \)
\( a=3 \)
\( a=0.36 \)
\( a=16 \)
Definite integral
1003027713
Level:
A
Which of the given values of \( a \) makes the statement true?
\[ a\cdot\int\limits_0^{\frac{\pi}2}\cos x\,\mathrm{d}x=\int\limits_{2\pi}^{3\pi}\sin x\,\mathrm{d}x \]
\( a=2 \)
\( a=\pi \)
\( a=4 \)
\( a=1 \)
1003027712
Level:
A
Compare two definite integrals \( I_1 = \int\limits_1^2 \frac1x\,\mathrm{d}x \) and \( I_2 = \int\limits_2^4 \frac1x\,\mathrm{d}x \).
\( I_1 \) is equal to \( I_2 \).
\( I_2 \) is twice as big as \( I_1 \).
\( I_1 \) is twice as big as \( I_2 \).
\( I_1 \) is \( 4 \) times as big as \( I_2 \).
1003027711
Level:
A
Compare two definite integrals \( I_1 = \int\limits_0^5 0.6x\,\mathrm{d}x \) and \( I_2 = \int\limits_0^5 1.8x\,\mathrm{d}x \).
\( I_2 \) is \( 3 \) times as big as \( I_1 \).
\( I_1 \) is \( 3 \) times as big as \( I_2 \).
\( I_2 \) is \( 1.2 \) multiple of \( I_1 \).
\( I_2 \) is \( 30 \) times as big as \( I_ 1 \).
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
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
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
1003027707
Level:
A
Which of the given values of \( a \) makes the statement true?
\[ \int\limits_0^51.6x\,\mathrm{d}x-a = \int\limits_0^50.6x\,\mathrm{d}x \]
\( a=12.5 \)
\( a=1 \)
\( a=13.5 \)
\( a=8 \)
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
\( \frac{\pi}6 \)
1003027705
Level:
A
How much smaller is \( \int\limits_0^{1} x^{15}\,\mathrm{d}x \) than \( \int\limits_0^{1} x^{5}\,\mathrm{d}x \)?
\( \frac5{48} \)
\( \frac{11}{48} \)
\( \frac5{32} \)
\( \frac{11}{32} \)