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Integrals of Trig Functions quiz

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  • What is the integral of cos(x) with respect to x?
    The integral of cos(x) dx is sin(x) + c.
  • What is the integral of sin(x) with respect to x?
    The integral of sin(x) dx is -cos(x) + c.
  • Which rule allows you to split the integral of a sum into the sum of integrals?
    The sum and difference rule allows you to split the integral of a sum into the sum of integrals.
  • How does the constant multiple rule simplify integrating 3sin(x) + 2cos(x)?
    You can pull out the constants and integrate each term separately: 3∫sin(x)dx + 2∫cos(x)dx.
  • What is the integral of sec(x)tan(x) with respect to x?
    The integral of sec(x)tan(x) dx is sec(x) + c.
  • What is the integral of cosec^2(x) (csc^2(x)) with respect to x?
    The integral of csc^2(x) dx is -cot(x) + c.
  • If the derivative of tan(x) is sec^2(x), what is the integral of sec^2(x)?
    The integral of sec^2(x) dx is tan(x) + c.
  • What is the integral of csc(x)cot(x) with respect to x?
    The integral of csc(x)cot(x) dx is -csc(x) + c.
  • How do you find the integral of a trigonometric function using its derivative?
    You reverse the process of differentiation, using the known derivatives of trig functions.
  • What is the result of integrating 7sec(x)tan(x) - csc^2(x) with respect to x?
    The result is 7sec(x) + cot(x) + c.
  • Why is it important to remember the derivatives of trig functions when integrating?
    Because integration is the reverse of differentiation, knowing derivatives helps you find integrals quickly.
  • What is always added to the result of an indefinite integral?
    The constant of integration, c, is always added.
  • If the derivative of cos(x) is -sin(x), what is the integral of sin(x)?
    The integral of sin(x) dx is -cos(x) + c.
  • How do you integrate a sum like a*sin(x) + b*cos(x)?
    Integrate each term separately using the constant multiple rule: a∫sin(x)dx + b∫cos(x)dx.
  • What is the integral of -sin(x) with respect to x?
    The integral of -sin(x) dx is cos(x) + c.