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Calculus practice

Trigonometric Integration worksheets

Practice six direct trigonometric antiderivative patterns with exact constant coefficients and unit or affine arguments in radians.

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Apply the matching trigonometric antiderivative rule, adjust for the constant derivative of the argument, and include + C.

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Reverse a measured derivative pattern

Match the original integrand to one of six standard trigonometric derivatives, then divide its coefficient by the signed derivative coefficient of the affine argument.

Learning objective

What this activity builds

Recognize a standard trigonometric derivative pattern, divide by the signed derivative coefficient of its affine argument, and include + C on the original domain.

Worked example

Find the indefinite integral of 2 cos(3x - 1) dx.

(2/3)sin(3x - 1) + C

Since d/dx sin(3x - 1) = 3cos(3x - 1), divide the original coefficient 2 by 3.

Teaching notes

Make the practice count

  • Identify the reverse-derivative pattern before adjusting its coefficient.
  • Include the derivative sign for cosine, cotangent and cosecant.
  • Retain zeros excluded by the original tangent, cotangent, secant or cosecant integrand.

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Math SheetNameScoreTeacherDateTrigonometric IntegrationApply the matching trigonometric antiderivative rule, adjust for the constant derivative of the argument, and include + C.1.-3·secx2dx2.-1·secx·tanxdx3.-2·cosxdx4.-1·cscx2dx5.-23·cscx·cotxdx6.-2·sinxdx7.-32·sec-2·x·tan-2·xdx8.23·sec-3+x2dx9.-1·cos3-3·xdx10.-3·csc-3-x2dxAll angles are in radians. Respect the original integrand domain.math-sheet.comPage 1 of 1

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