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University Integral Calculus Problem Solving Quiz

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University Integral Calculus Problem Solving Quiz

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Questions and Answers

What is the integral of $3x^2 + 2x - 5$ with respect to $x$?

$x^3 + x - 5 + C$

$x^3 + x^2 - 5x^2 + C$

$x^3 + x^2 - 5x + C$ (correct)

$x^3 + x - 5x + C$

What is the integral of $\sin^2(x) \cos(x)$ with respect to $x$?

$\frac{1}{3} \sin^3(x) + C$ (correct)

$\frac{1}{2} \sin^3(x) + C$

$\frac{1}{2} \sin^2(x) + C$

$\frac{1}{3} \sin^2(x) + C$

If $f(x) = \int (e^{2x} + 3x), dx$ and $f(0) = 4$, what is the value of $f(1)$?

$4e^2+10$

$10e^2-4$

$10e^2+4$

$4e^2-10$ (correct)

When converting from binary to octal, how many binary digits are equivalent to one octal digit?

3 Signup and view all the answers

In the hexadecimal number system, what is the base of the system?

16 Signup and view all the answers

What is the value of $101101_2$ when converted to decimal?

57 Signup and view all the answers

When converting from binary to hexadecimal, how many binary digits are equivalent to one hexadecimal digit?

4 Signup and view all the answers

What is the value of $110110_2$ when converted to octal?

$26_8$ Signup and view all the answers

What is the value of $10001100_2$ when converted to decimal?

$156_{10}$ Signup and view all the answers

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.

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Description

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.