9000065609
Level:
A
Find the area of the region bounded by the curves
\(y = -x + 3\),
\(y = x^{2} - 3x\).
\(\frac{32}
{3} \)
\(8\)
\(\frac{8}
{3}\)
\(\frac{16}
{3} \)
Applications of definite integral
9000065608
Level:
A
Using integrals write formula for the area of the shaded region.
\(\int _{a}^{b}(f(x) - g(x))\, \mathrm{d}x +\int _{ b}^{c}(g(x) - f(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(g(x) - f(x))\, \mathrm{d}x +\int _{ b}^{c}(g(x) - f(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(f(x) - g(x))\, \mathrm{d}x +\int _{ b}^{c}(f(x) - g(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(f(x) + g(x))\, \mathrm{d}x +\int _{ b}^{c}(f(x) - g(x))\, \mathrm{d}x\)
9000065601
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x) = x + 3\)
and lines \(x = -1\)
and \(x = 1\).
\(6\)
\(2\)
\(4\)
\(8\)
9000065610
Level:
A
Using definite integral find the area of the triangle defined by the following three
inequalities
\[
\begin{aligned}y& > 0, &
\\y& < x + 3,
\\y& < 3 - x.
\\ \end{aligned}
\]
\(\int _{-3}^{0}(x + 3)\, \mathrm{d}x +\int _{ 0}^{3}(3 - x)\, \mathrm{d}x\)
\(\int _{0}^{3}(x + 3)\, \mathrm{d}x\)
\(\int _{-3}^{3}(3 - x)\, \mathrm{d}x\)
\(\int _{-3}^{0}(3 - x)\, \mathrm{d}x +\int _{ 0}^{3}(x + 3)\, \mathrm{d}x\)
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 \(x = 1\).
\(12\)
\(6\)
\(8\)
\(10\)
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 \(x =\pi \).
\(1\)
\(\frac{3}
{4}\)
\(\frac{\sqrt{3}}
{2} \)
\(2\)