C

1003107904

Level: 
C
Solve the indefinite integral \[ \int\left(ab\mathrm{e}^c-bx^2+5^b-\sin ⁡c\right) \mathrm{d}b \] of a real-valued function, where \( x \), \( a \), \( c \) are real numbers.
\( 0.5a\mathrm{e}^cb^2-\frac{b^2}2 x^2+\frac{5^b}{\ln⁡5} -b\sin ⁡c+k \), \( k\in\mathbb{R} \)
\( 0.5a\mathrm{e}^cb^2-\frac{b^2}2\cdot\frac{x^3}3+\frac{5^b}{\ln⁡5} -b \sin⁡ c+k \), \( k\in\mathbb{R} \)
\( a\mathrm{e}^c-2bx+5^b-\sin ⁡c+k \), \( k\in\mathbb{R} \)
\( a\mathrm{e}^c-bx^2+5^b-b\sin c+k \), \( k\in\mathbb{R} \)

1003107903

Level: 
C
Solve the indefinite integral \[ \int\left( ab\mathrm{e}^c-bx^2+5^b-\sin ⁡c\right)\mathrm{d}a \] of a real-valued function, where \( x \), \( b \), \( c \) are real numbers.
\( \frac{a^2 b\mathrm{e}^c}2-abx^2+a5^b-a\sin⁡ c+k \), \( k\in\mathbb{R} \)
\( \frac{a^2}2b\mathrm{e}^c+k \), \( k\in\mathbb{R} \)
\( b\mathrm{e}^c-bx^2+5^b-\sin⁡ c+k \), \( k\in\mathbb{R} \)
\( ab\mathrm{e}^c-b\frac{x^3}3+k \), \( k\in\mathbb{R} \)

1003107902

Level: 
C
Solve the indefinite integral \[ \int\left(ab\mathrm{e}^c-bx^2+5^b-\sin ⁡c \right)\mathrm{d}x \] of a real-valued function, where \( a \), \( b \), \( c \) are real numbers.
\( ab\mathrm{e}^c x-b\frac{x^3}3+5^b x-x \sin c+k \), \( k\in\mathbb{R} \)
\( -b\frac{x^3}3+k \), \( k\in\mathbb{R} \)
\( ab\mathrm{e}^c-2b+5^b-\sin c+k \), \( k\in\mathbb{R} \)
\( ab\mathrm{e}^c x-2bx+5^b x-x \sin c+k \), \( k\in\mathbb{R} \)

1003107901

Level: 
C
Solve the indefinite integral \[ \int\sin^3 x\cos^2x\,\mathrm{d}x \] of a real-valued function using a suitable substitution.
\( \frac{\cos^5⁡x}5-\frac{\cos^3⁡x}3+c \)
\( -\frac{\cos^5⁡x}5+\frac{\cos^3⁡x}3+c \)
\( \frac{\cos^5⁡x}5+\frac{\cos^3⁡x}3+c \)
\( -\frac{\cos^5⁡x}5-\frac{\cos^3⁡x}3+c \)

1003158507

Level: 
C
Let there be a row of five yellow cubes lying side by side. The first cube has an edge length of \( 100\,\mathrm{cm} \) and each next cube has an edge length by \( 10\,\mathrm{cm} \) shorter than the previous one. Let there be a second row of five blue cubes lying side by side. The first blue cube has an edge length of \( 100\,\mathrm{cm} \) and each next cube has an edge length by \( 10\% \) smaller than the previous one. What is the difference between the length of these two rows?
\( 9.51\,\mathrm{cm} \)
\( 34.51\,\mathrm{cm} \)
\( 0\,\mathrm{cm} \)
\( 20\,\mathrm{cm} \)
\( 20.51\,\mathrm{cm} \)
Error | math4u.vsb.cz

Error

The website encountered an unexpected error. Please try again later.