9000065601
Level:
A
Find the area of the region bounded by
\(x\)-axis,
graph of \(f(x) = x + 3\)
and lines \(x = -1\)
and \(x = 1\).
\(6\)
\(2\)
\(4\)
\(8\)
Applications of definite integral
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 \(x =\pi \).
\(1\)
\(\frac{3}
{4}\)
\(\frac{\sqrt{3}}
{2} \)
\(2\)
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
\(y = 3\).
\(6 -\frac{4}
{\ln 3}\)
\(3 -\frac{2}
{\ln 3}\)
\(3 + \frac{4}
{\ln 3}\)
\(6 -\frac{2}
{\ln 3}\)