1003108104
Level:
B
Evaluate the integral \( \int\limits_{-2}^0 (x+2)^3\,\mathrm{d}x \).
\( 4 \)
\( 28 \)
\( -28 \)
\( 12 \)
Definite integral
1003108103
Level:
B
Evaluate the integral \( \int\limits_{-1}^1\frac{x^2+3x-10}{x-2}\,\mathrm{d}x \).
\( 10 \)
\( 6 \)
\( 8 \)
\( 12 \)
1003108102
Level:
B
Evaluate the integral \( \int\limits_{-1}^1 \left(x^2-x\right)(x+1)\,\mathrm{d}x \).
\( 0 \)
\( \frac12 \)
\( 2 \)
\( 1 \)
1003108101
Level:
B
Evaluate the integral \( \int\limits_1^4\frac{\sqrt x-x+x^2}x\,\mathrm{d}x \).
\( 6.5 \)
\( 5.5 \)
\( 9.5 \)
\( 14.5 \)
1003118805
Level:
B
Evaluate the integral \( \int\limits_{-5}^5 f(x)\,\mathrm{d}x \), where \( f(x)=x^2+2 \) for \( x\in[-5;1] \) and \( f(x)=3 \) for \( x\in[ 1;5] \).
\( 66 \)
\( \frac73 \)
\( \frac{25}3 \)
\( 42 \)
1003118804
Level:
B
Evaluate the integral \( \int\limits_{-3}^2 f(x)\,\mathrm{d}x \), where \( f(x)=x^{-4} \) for \( x\in\left[-3;-\frac12\right] \) and \( f(x)=12.8-6.4x \) for \( x\in\left[ -\frac12;2\right]\). (rounded to \( 2 \) decimal places)
\( 22.65 \)
\( 43.\overline{8} \)
\( 44.\overline{1} \)
\( 29.7\overline{1} \)
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 \( -\frac12 \).
\( 1 \)
\( 3 \)
\( -1 \)
\( 2 \)
1003118802
Level:
B
Find positive real numbers \( a \) and \( b \), \( a \), \( b>0 \), such that \( b-a=6 \) and \( \int\limits_a^b(4x-6)\,\mathrm{d}x=60 \).
\( a=1 \), \( b=7 \)
\( a=7 \), \( b=1 \)
\( a=24 \), \( b=30 \)
\( a=1.5 \), \( b=7.5 \)
1003118801
Level:
B
Which of the following formulas is not equal to \( \int\limits_4^8\frac{3x+1}{x^2-x-6}\,\mathrm{d}x \)?
\( \int\limits_4^8\frac2{x-3}\,\mathrm{d}x -\int\limits_4^8\frac1{x+2}\,\mathrm{d}x \)
\( \int\limits_4^8\frac2{x-3}\,\mathrm{d}x + \int\limits_4^8\frac1{x+2}\,\mathrm{d}x \)
\( \int\limits_4^6\frac{3x+1}{x^2-x-6}\,\mathrm{d}x + \int\limits_6^8\frac{3x+1}{x^2-6-x}\,\mathrm{d}x \)
\( \int\limits_8^4\frac{-1-3x}{x^2-x-6}\,\mathrm{d}x \)
1003108008
Level:
A
Find the value of \( p \) such that \[ \int\limits_{-2}^3\left(3x^2-5x^4+4x+p\right)\mathrm{d}x=-255. \]
\( -5 \)
\( 5 \)
\( 3 \)
No such \( p \) exists.