1003118904
Level:
B
Evaluate the definite integral.
\[ \int\limits_{-\frac{\pi}2}^{\pi}x\cdot\sin x\,\mathrm{d}x \]
\( \pi+1 \)
\( \pi-1 \)
\( \frac{\pi+2}2 \)
\( \frac{\pi}2 \)
Definite integral
1103118803
Level:
B
The picture shows a graph of a power function \( f(x) \). Find the value of the definite integral of this function between \( -1 \) and \( -\frac12 \).
\( 1 \)
\( 3 \)
\( -1 \)
\( 2 \)
2010001104
Level:
B
Evaluate the definite integral \( \int\limits_1^4\frac{\sqrt x+x^2-x^3}{x^2}\,\mathrm{d}x \).
\( -3.5 \)
\( -11 \)
\( -5.5 \)
\( -3\)
2010001105
Level:
B
Evaluate the definite integral \( \int\limits_{-1}^1 (x+1)^4\,\mathrm{d}x \).
\( 6.4 \)
\( 32\)
\( 0.2 \)
\( 8\)
2010001106
Level:
B
Evaluate the definite integral \( \int\limits_2^3\frac{x+2}{x-1}\,\mathrm{d}x \).
\( 1+\ln8 \)
\( -2+\ln8\)
\( 1+\ln\left(\frac32\right)^3 \)
\( 1+(\ln2)^3 \)
2010001201
Level:
B
Evaluate the definite integral \( \int\limits_{\frac{\pi}6}^{\frac{\pi}3}\frac{\mathrm{cotg}\,b}{\sin2b}\,\mathrm{d}b \).
\( \frac{\sqrt3}3 \)
\( -2\sqrt3 \)
\( 2\sqrt3 \)
\( -\sqrt3 \)
2010001202
Level:
B
Evaluate the definite integral.
\[ \int\limits_{-\pi}^{\frac{\pi}2}x\cdot\cos x\,\mathrm{d}x \]
\( \frac{\pi+2}{2} \)
\(\pi +1\)
\(\frac{\pi}2\)
\( \frac{\pi}2-1\)
2010001203
Level:
B
Evaluate the definite integral.
\[
\int _{\frac{2}{3}}^{3} \frac{1}
{3x -1}\, \text{d}x
\]
\(\ln 2\)
\(\ln 1\)
\(\ln 8\)
\(3\ln 8\)
2010001204
Level:
B
Evaluate the definite integral.
\[
\int _{-1}^{2} \frac{-2x}
{4+x^{2}}\, \text{d}x
\]
\(\ln \frac{5}
{8}\)
\(\ln 40\)
\(\ln \frac{8}
{5}\)
\(-\ln 40\)
9000150405
Level:
B
Evaluate the following definite integral.
\[
\int _{-1}^{3} \frac{1}
{2x + 3}\, \text{d}x
\]
\(\ln 3\)
\(\ln 1\)
\(\ln 9\)
\(2\ln 9\)