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.
A
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.
2000000901
Level:
A
Compare definite integrals \(I_1 = \int\limits_0^{\frac{\pi}{4}}\mathrm{tg}\,x \,\mathrm{d}x\) and \(I_2= \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}}\mathrm{cotg}\, x\,\mathrm{d}x\).
\(I_1=I_2\)
\(I_1 > I_2\)
\(I_1 < I_2\)
These integrals cannot be compared.
2010000003
Level:
A
Evaluate the definite integral. \[ \int\limits_{-\frac{\pi}6}^{\frac{\pi}6}(\cos x-\sin x )\,\mathrm{d}x \]
\( 1 \)
\( \sqrt3 \)
\( 1+\sqrt3 \)
\(0\)
2010000002
Level:
A
Evaluate the definite integral. \[ \int\limits_0^1\left(\ln5 - \frac{7}{5}\sqrt[5]{x^2}+x^4\right)\mathrm{d}x \]
\( \ln 5-\frac{4}{5} \)
\(\ln 5-\frac{1}{5} \)
\( -\frac{4}{5} \)
\(- \frac{1}{5} \)
2010000001
Level:
A
Vypočítejte určitý integrál. \[ \int\limits_1^2\left(5^x \cdot\ln5 -x^5-4x\right)\mathrm{d}x \]
\( \frac{7}{2} \)
\( -\frac{5}{2} \)
\(- \frac{1}{2} \)
\( -\frac{5}{6} \)
2000000810
Level:
A
Consider a function \(f(x)=ax+b\), where \(x \in (-1;4)\) and the range of \(f\) is \((-3;2)\). Find the coefficients \(a\) and \(b\).
\(a=-1,~b=1\)
\(a=-1,~b=4\)
\(a=2,~b=-3\)
\(a=1,~b=2\)
2000000809
Level:
A
Consider the linear function \(f(x)=3x-2\). Which of the given points belongs to the graph of \(f\)?
\([-2;-8]\)
\([-2;0]\)
\(\left[0;-\frac{2}{3}\right]\)
\(\left[0;-\frac{4}{3}\right]\)
2000000808
Level:
A
Consider the linear function \(f(x)=-6x-2\). Choose the correct statement.
\(f(3)=-20\)
\(f(-2)=-14\)
\(f(10)=-2\)
\(f(-2)=0\)
2000000807
Level:
A
Consider the linear function \(f(x)=-2x+6\). Choose the correct statement.
The function \(f\) is one-to-one.
The function \(f\) is even.
The function \(f\) is odd.
The function \(f\) is increasing.