9 Questions
What is the integral of $3x^2 + 2x - 5$ with respect to $x$?
$x^3 + x^2 - 5x + C$
What is the integral of $\sin^2(x) \cos(x)$ with respect to $x$?
$\frac{1}{3} \sin^3(x) + C$
If $f(x) = \int (e^{2x} + 3x), dx$ and $f(0) = 4$, what is the value of $f(1)$?
$4e^2-10$
When converting from binary to octal, how many binary digits are equivalent to one octal digit?
3
In the hexadecimal number system, what is the base of the system?
16
What is the value of $101101_2$ when converted to decimal?
57
When converting from binary to hexadecimal, how many binary digits are equivalent to one hexadecimal digit?
4
What is the value of $110110_2$ when converted to octal?
$26_8$
What is the value of $10001100_2$ when converted to decimal?
$156_{10}$
Study Notes
Integration
- The integral of $3x^2 + 2x - 5$ with respect to $x$ is a fundamental concept in calculus.
- The integral of $\sin^2(x) \cos(x)$ with respect to $x$ is another important integration problem.
Indefinite Integrals
- If $f(x) = \int (e^{2x} + 3x), dx$, then the value of $f(0)$ is given as 4.
- The value of $f(1)$ can be determined using the definition of the indefinite integral.
Number Systems
- When converting from binary to octal, 3 binary digits are equivalent to one octal digit.
- The base of the hexadecimal number system is 16.
- 1 hexadecimal digit is equivalent to 4 binary digits when converting from binary to hexadecimal.
Binary Conversion
- The value of $101101_2$ in decimal is 45.
- The value of $110110_2$ in octal is 66.
- The value of $10001100_2$ in decimal is 132.
Test your integral calculus skills with these problem-solving questions related to trigonometry. Practice finding the integral of polynomial expressions and trigonometric functions, as well as evaluating definite integrals using the given initial condition.
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