1103068002
Level:
A
Define an unknown real positive constant \( a \) so that the yellow surface indicated in the picture has an area of \( 9 \) square units.
\( a=3 \)
\( a=27 \)
\( a=9 \)
\( a=1 \)
Applications of definite integral
1103068003
Level:
A
Find the missing real positive constant \( a \) so that the area of the yellow triangle indicated in the picture is \( 12 \) square units.
\( a=\frac23 \)
\( a=\frac43 \)
\( a=1 \)
The constant \( a \) can not be determined from the picture.
1103068004
Level:
A
Find the missing real constant \( a \) so that the ratio of the green and the red area indicated in the picture is \( 4:1 \).
\( a=-\frac{5}3\pi \)
\( a=-2\pi \)
\( a=-\pi \)
\( a=-\frac{5}4\pi \)
1103068005
Level:
A
Find the missing real constant \( a \) so that the green area and the red area indicated in the picture do equal.
\( a=-2\pi \)
\( a=-\frac32\pi \)
\( a=-\frac{\pi}2 \)
\( a=-3\pi \)
1103068101
Level:
A
Find the area of the yellow region that is bounded by the parabola and the line as is indicated in the picture. Read all the needed values from the picture.
\( 4.5 \)
\( 22.5 \)
\( 3.75 \)
\( 10.25 \)
1103068102
Level:
A
Find the area of the yellow triangle ABC indicated in the picture. Read all the needed values from the picture.
\( 10 \)
\( 11 \)
\( 9.5 \)
\( 10.5 \)
1103068103
Level:
A
Find the area of the yellow region indicated in the picture.
\( 2\sqrt2 \)
\( 2\sqrt3 \)
\( \sqrt2 \)
\( 4\sqrt2 \)
1103108901
Level:
A
Which of the given expressions does not describe the area of the region highlighted in yellow? (See the picture.)
$4\cdot\int\limits_0^{\frac{\pi}4}4\sin x\,\mathrm{d}x$
$4\cdot\int\limits_0^{\pi}\sin x\,\mathrm{d}x$
$8\cdot\int\limits_0^{\pi}\frac{\sin x}2\,\mathrm{d}x$
$\int\limits_0^{\frac{\pi}2}16\cdot\frac{\sin x}2\,\mathrm{d}x$
1103108902
Level:
A
Which of the given expressions does not describe the area of the region highlighted in yellow? (See the picture.)
$\int\limits_1^3\frac1x\,\mathrm{d}x$
$2\int\limits_1^3\frac1x\,\mathrm{d}x$
$\int\limits_1^4\frac2x\,\mathrm{d}x-\int\limits_3^4\frac2x\,\mathrm{d}x$
$\int\limits_1^3\frac1x\,\mathrm{d}x-\int\limits_1^3-\frac1x\,\mathrm{d}x$
1103108903
Level:
A
Which of the given pictures shows the shaded region of the biggest area?
