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Lesson Worksheet: Trigonometric Integrals Mathematics

In this worksheet, we will practice evaluating integrals of the products of trigonometric terms using trigonometric identities.

Q1:

Determine 39𝑥𝑥tand.

  • A13(9𝑥+9𝑥)+tanC
  • B13(9𝑥9𝑥)+tanC
  • C139𝑥+tanC
  • D279𝑥+secC

Q2:

Determine 8𝑥+11𝑥tand.

  • A3𝑥8𝑥+tanC
  • B3𝑥16𝑥+tanC
  • C19𝑥16𝑥+tanC
  • D8𝑥+tanC
  • E19𝑥8𝑥+tanC

Q3:

Determine 8𝑥𝑥cosd.

  • A22𝑥+sinC
  • B4𝑥22𝑥+sinC
  • C22𝑥+sinC
  • D4𝑥+22𝑥+sinC
  • E4𝑥82𝑥+sinC

Q4:

Determine 169𝑥9𝑥𝑥sincosd.

  • A14418𝑥+cosC
  • B899𝑥+cosC
  • C4918𝑥+cosC
  • D899𝑥+cosC
  • E4918𝑥+cosC

Q5:

Determine ((𝑥)+(𝑥))𝑥cotcscd.

  • A2(𝑥)+𝑥2(𝑥)+cotcscC
  • B2(𝑥)𝑥2(𝑥)+cotcscC
  • C2(𝑥)𝑥2(𝑥)+tancscC
  • D2(𝑥)𝑥+2(𝑥)+cotcscC
  • E2(𝑥)+𝑥+2(𝑥)+cotsecC

Q6:

Determine (38𝑥38𝑥)𝑥sincosd.

  • A9𝑥91616𝑥+cosC
  • B9𝑥+916𝑥+cosC
  • C9𝑥916𝑥+cosC
  • D9𝑥+91616𝑥+cosC

Q7:

Determine (1𝑥)(𝑥)𝑥cossind.

  • A2(𝑥)2(𝑥)+𝑥+csccotC
  • B2(𝑥)2(𝑥)𝑥+csccotC
  • C2(𝑥)+2(𝑥)𝑥+csccotC
  • D2(𝑥)2(𝑥)𝑥+csccotC
  • E2(𝑥)+2(𝑥)𝑥+csccotC

Q8:

Evaluate 𝑥𝑥𝑥sincosd.

  • A𝜋4
  • B𝜋4
  • C𝜋2
  • D𝜋8
  • E𝜋8

Q9:

Evaluate 𝜃(1+𝜃)𝜃sincosd.

  • A4𝜋
  • B14𝜋
  • C14𝜋
  • D𝜋4
  • E4+𝜋

Q10:

By rewriting 3𝑥+5𝑥sincos using the Pythagorean identity and the double angle formula for cosine, evaluate 3𝑥+5𝑥𝑥sincosd.

  • A𝜋
  • B4𝜋
  • C2𝜋
  • D2𝜋
  • E4𝜋

This lesson includes 56 additional questions and 572 additional question variations for subscribers.

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