Integration Practice: Exponential, Trigonometric, and Reciprocal Functions
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Questions and Answers

What is the integral of $e^{2x}$ with respect to $x$?

  • $\frac{1}{2}e^{2x}$
  • $\frac{1}{2}e^{2x} + C$ (correct)
  • $2e^{2x} + C$
  • $e^{2x} + C$

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

  • $\frac{x}{2} - \frac{1}{4}\sin(2x) + C$ (correct)
  • $-\frac{x}{2} - \frac{1}{4}\sin(2x) + C$
  • $-\frac{x}{2} + \frac{1}{4}\sin(2x)$
  • $\frac{x}{2} + \frac{1}{4}\sin(2x)$

    • What is the integral of $\frac{1}{x^2}$ with respect to $x$?

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

    • Study Notes

    Integration of Mathematical Functions

    • The integral of e^(2x) with respect to x is (1/2)e^(2x) + C, where C is the constant of integration.
    • The integral of sin^2(x) with respect to x is (x/2) - (sin(2x))/4 + C, where C is the constant of integration.
    • The integral of 1/x^2 with respect to x is -1/x + C, where C is the constant of integration.

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    Test your integration skills with these practice questions on finding the integrals of exponential, trigonometric, and reciprocal functions with respect to x.

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