2010001105
Level:
B
Evaluate the definite integral \( \int\limits_{-1}^1 (x+1)^4\,\mathrm{d}x \).
\( 6.4 \)
\( 32\)
\( 0.2 \)
\( 8\)
Definite integral
2010001104
Level:
B
Evaluate the definite integral \( \int\limits_1^4\frac{\sqrt x+x^2-x^3}{x^2}\,\mathrm{d}x \).
\( -3.5 \)
\( -11 \)
\( -5.5 \)
\( -3\)
2010001103
Level:
A
Evaluate the definite integral. \[ \int\limits_1^3\left(\frac3x-\frac x3+x^3\right)\mathrm{d}x \]
\( \frac{56}{3}+\ln 27 \)
\( \frac{56}{3}+\ln 9 \)
\( \frac{65}{3} +\ln 27 \)
\( \frac{56}{3} \)
2010001102
Level:
A
Evaluate the definite integral. \[ \int\limits_{\frac{\pi}6}^{\frac{\pi}3}\left(\frac3{\sin^2x} -\frac6{\cos^2x}\right)\mathrm{d}x \]
\( -2\sqrt3 \)
\( 2\sqrt3 \)
\( 0 \)
\( 12\sqrt3 \)
2010001101
Level:
A
Evaluate the definite integral.
\[ \int\limits_0^1\left(4\sqrt[3]{x}-4x^3+2\mathrm{e}^x\right)\mathrm{d}x \]
\( 2\mathrm{e} \)
\( 4+2\mathrm{e} \)
\( 0 \)
\( -2\mathrm{e} \)
2000000906
Level:
A
Evaluate the definite integral \(\int\limits_{\pi}^{2\pi}\sin x\,\mathrm{d}x\).
\(-2\)
\(-1\)
\(-\frac{\pi}{2}\)
\(0\)
2000000905
Level:
A
Evaluate the definite integral \(\int\limits_1^{2}x\, \mathrm{d}x\).
\(\frac{3}{2}\)
\(1\)
\(6\)
\(3\)
2000000904
Level:
A
Evaluate the definite integral \(\int\limits_0^{1}x^3\,\mathrm{d}x\).
\(\frac{1}{4}\)
\(1\)
\(\frac{1}{3}\)
\(3\)
2000000903
Level:
A
Compare definite integrals \(I_1 = \int\limits_0^{1}x^2 \,\mathrm{d}x\) and \(I_2= \int\limits_{0}^{1}(1-x^2)\,\mathrm{d}x\).
\( I_1 < I_2 \)
\(I_1 =I_2\)
\(I_1 >I_2\)
These integrals cannot be compared.
2000000902
Level:
A
Compare definite integrals \(I_1 = \int\limits_{-10}^{10}x^4\,\mathrm{d}x\) and \(I_2= \int\limits_{-10}^{10}x^5\,\mathrm{d}x\).
\(I_1 > I_2\)
\(I_1 = I_2\)
\(I_1 < I_2\)
These integrals cannot be compared.