2010008005 Level: ACompare the two definite integrals \( I_1 = \int_1^2 \left( x^2-x\right) \mathrm{d}x\) and \( I_2 = \int_2^1 \left( x-x^2\right) \mathrm{d}x\).\( I_1 =I_2\)\( I_1 > I_2\)\( I_1 < I_2 \)These integrals cannot be compared.
2010008004 Level: ACompare the two definite integrals \( I_1 = \int_0^1 \left( x^6\cos^2x-20\right) \mathrm{d}x\) and \( I_2 = \int_0^1 \left( 20-x^6\cos^2x\right) \mathrm{d}x\).\( I_1 < I_2\)\( I_1 = I_2\)\( I_1 > I_2 \)These integrals cannot be compared.
2010008003 Level: ACompare the two definite integrals \( I_1 = \int_0^1 \left( 10-x^4\sin^2x\right) \mathrm{d}x\) and \( I_2 = \int_0^1 \left( x^4\sin^2x-10\right) \mathrm{d}x\).\( I_1 > I_2\)\( I_1 = I_2\)\( I_1 < I_2 \)These integrals cannot be compared.
2010008002 Level: ACompare the two definite integrals \( I_1 = \int_0^3 \frac{x^3}{3^x} \mathrm{d}x\) and \( I_2 = \int_3^0 \frac{x^3}{3^x}\ \mathrm{d}x\).\( I_1 > I_2\)\( I_1 = I_2\)\( I_1 < I_2 \)These integrals cannot be compared.
2010008001 Level: ACompare the two definite integrals \( I_1 = \int_0^2 x^5 \cdot 2^x \mathrm{d}x\) and \( I_2 = \int_2^0 x^5 \cdot 2^x \mathrm{d}x\).\( I_1 > I_2\)\( I_1 = I_2\)\( I_1 < I_2 \)These integrals cannot be compared.
2010001204 Level: BEvaluate the definite integral. \[ \int _{-1}^{2} \frac{-2x} {4+x^{2}}\, \text{d}x \]\(\ln \frac{5} {8}\)\(\ln 40\)\(\ln \frac{8} {5}\)\(-\ln 40\)
2010001203 Level: BEvaluate the definite integral. \[ \int _{\frac{2}{3}}^{3} \frac{1} {3x -1}\, \text{d}x \]\(\ln 2\)\(\ln 1\)\(\ln 8\)\(3\ln 8\)
2010001202 Level: BEvaluate the definite integral. \[ \int\limits_{-\pi}^{\frac{\pi}2}x\cdot\cos x\,\mathrm{d}x \]\( \frac{\pi+2}{2} \)\(\pi +1\)\(\frac{\pi}2\)\( \frac{\pi}2-1\)
2010001201 Level: BEvaluate the definite integral \( \int\limits_{\frac{\pi}6}^{\frac{\pi}3}\frac{\mathrm{cotg}\,b}{\sin2b}\,\mathrm{d}b \).\( \frac{\sqrt3}3 \)\( -2\sqrt3 \)\( 2\sqrt3 \)\( -\sqrt3 \)
2010001106 Level: BEvaluate the definite integral \( \int\limits_2^3\frac{x+2}{x-1}\,\mathrm{d}x \).\( 1+\ln8 \)\( -2+\ln8\)\( 1+\ln\left(\frac32\right)^3 \)\( 1+(\ln2)^3 \)