2010012602
Level:
A
Find the area of the region bounded by the curves
\(y = 2^{x}\),
\(y = 2^{-x}\) and
\(y = 4\).
\(16 -\frac{6}
{\ln 2}\)
\(16 -\frac{10}
{\ln 2}\)
\(8 -\frac{5}
{\ln 2}\)
\(16 +\frac{6}
{\ln 2}\)
Applications of definite integral
9000065601
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x) = x + 3\)
and lines \(x = -1\)
and \(x = 1\).
\(6\)
\(2\)
\(4\)
\(8\)
9000065602
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x)= x^{2} + 3\)
and lines \(x = -2\)
and \(x = 1\).
\(12\)
\(6\)
\(8\)
\(10\)
9000065603
Level:
A
Find the area of the region bounded by the curves
\(y = 0\),
\(y = x^{3}\),
\(x = 1\) and
\(x = 3\).
\(20\)
\(22\)
\(24\)
\(26\)
9000065604
Level:
A
Find the area of the region bounded by the graph of
\(f(x)=\cos x\) on
\(\left [ \frac{\pi }{2};\pi \right ] \) and
lines \(y = 0\)
and \(x =\pi \).
\(1\)
\(\frac{3}
{4}\)
\(\frac{\sqrt{3}}
{2} \)
\(2\)
9000065605
Level:
A
Find the area of the region bounded by the curves
\(y = -2x\) and
\(y = -x^{2} + 3\).
\(\frac{32}
{3} \)
\(\frac{29}
{3} \)
\(\frac{31}
{3} \)
\(\frac{35}
{3} \)
9000065606
Level:
A
Find the area of the region bounded by the curves
\(y =\mathrm{e} ^{x}\),
\(y = -\mathrm{e}^{x} + 2\) and
\(x = -3\).
\(4 + \frac{2}
{\mathrm{e}^{3}} \)
\(4 + \frac{1}
{\mathrm{e}^{3}} \)
\(4 -\frac{2}
{\mathrm{e}^{3}} \)
\(4 -\frac{1}
{\mathrm{e}^{3}} \)
9000065607
Level:
A
Find the area of the region bounded by the curves
\(y = 3^{x}\),
\(y = 3^{-x}\) and
\(y = 3\).
\(6 -\frac{4}
{\ln 3}\)
\(3 -\frac{2}
{\ln 3}\)
\(3 + \frac{4}
{\ln 3}\)
\(6 -\frac{2}
{\ln 3}\)
9000065608
Level:
A
Using integrals write formula for the area of the shaded region.
\(\int _{a}^{b}(f(x) - g(x))\, \mathrm{d}x +\int _{ b}^{c}(g(x) - f(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(g(x) - f(x))\, \mathrm{d}x +\int _{ b}^{c}(g(x) - f(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(f(x) - g(x))\, \mathrm{d}x +\int _{ b}^{c}(f(x) - g(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(f(x) + g(x))\, \mathrm{d}x +\int _{ b}^{c}(f(x) - g(x))\, \mathrm{d}x\)
9000065609
Level:
A
Find the area of the region bounded by the curves
\(y = -x + 3\),
\(y = x^{2} - 3x\).
\(\frac{32}
{3} \)
\(8\)
\(\frac{8}
{3}\)
\(\frac{16}
{3} \)