1003108904
Level:
A
What is the area of the plain region bounded by the lines $x=2$, $x=3$ and the graphs of functions $f(x)=\sin x$ and $g(x)=\frac1{x^2}$? Round the result to three decimal digits.
$0.407$
$0.167$
$1.573$
$0.623$
Applications of definite integral
1003108905
Level:
A
Find the area of the plain region bounded by the curves $f(x)=x^5$ and $g(x)=x^9$ on the interval $[1;2]$.
$91.8$
$113.2$
$91.6$
$100.4$
1003108907
Level:
A
What are the lengths of a right triangle legs, if the triangle area is given by the expression $\int\limits_{-4}^1(0.8x+4.2)\,\mathrm{d}x-5$?
$5$ and $4$
$6$ and $3$
$4$ and $6$
$6$ and $5$
1003108908
Level:
A
What is the radius of a circle inscribed in a square, if the area of the square is given by the expression $\int\limits_1^6(6-x)\,\mathrm{d}x$ ?
$\frac{5\sqrt2}4$
$3\sqrt2$
$2\sqrt2$
$\frac{7\sqrt2}2$
1003124406
Level:
A
Calculate the area of a plane region bounded by the graphs of the functions $f(x)=x^2+2x+2$ and $g(x)=6-x^2$.
$9$
$21$
$15$
$\frac{59}3$
1003124410
Level:
A
Calculate the area of a plane region bounded by the graphs of the functions $f(x)=-\frac x{\pi}+1$ and $g(x)=-\sin x$, and by the lines $x=\pi$ and $x=0$.
$2+\frac{\pi}2$
$2-\frac{\pi}2$
$-2-\frac{\pi}2$
$\frac{2+\pi}2$
1103067901
Level:
A
Find the area of the yellow region indicated in the picture.
\( 6 \)
\( 0 \)
\( 3 \)
\( -6 \)
1103067902
Level:
A
Find the area of the region bounded by the curves \( y=x^3-5x^2+3x+5\text{, }x=0\text{, }x=1\text{, }y=-x+5 \) as indicated in the picture.
\( \frac7{12} \)
\( \frac{41}{12} \)
\( \frac{47}{12} \)
\( \frac5{12} \)
1103067903
Level:
A
Find the area of the yellow region indicated in the picture.
\( 8\pi \)
\( 6\pi \)
\( 2\pi \)
\( 10\pi \)
1103068001
Level:
A
Which of the following formulas does NOT express the area of the yellow triangle indicated in the picture?
\( \int\limits_1^ 6(-0.8x+5.8)\,\mathrm{d}x \)
\( \frac12\cdot(5-1)\cdot(6-1)\cdot\sin90^{\circ} \)
\( \frac{4\cdot5}2 \)
\( \int\limits_1^ 6(-0.8x+5.8)\,\mathrm{d}x-5 \)