Worksheet: Trigonometric Integrals

In this worksheet, we will practice evaluating the integral of a product of sines and cosines using trigonometric identities.

Q1:

Determine (84𝑥9𝑥)𝑥sinsind.

  • A45𝑥+413𝑥+sinsinC
  • B45𝑥413𝑥+sinsinC
  • C455𝑥41313𝑥+sinsinC
  • D455𝑥+41313𝑥+sinsinC
  • E205𝑥+5213𝑥+sinsinC

Q2:

Determine (64𝑥7𝑥)𝑥sinsind.

  • A33𝑥+311𝑥+sinsinC
  • B33𝑥311𝑥+sinsinC
  • CsinsinC3𝑥31111𝑥+
  • D3𝑥+31111𝑥+sinsinC
  • E93𝑥+3311𝑥+sinsinC

Q3:

Determine (55𝑥8𝑥)𝑥sinsind.

  • A523𝑥5213𝑥+sinsinC
  • B523𝑥+5213𝑥+sinsinC
  • C563𝑥+52613𝑥+sinsinC
  • D563𝑥52613𝑥+sinsinC
  • E1523𝑥65213𝑥+sinsinC

Q4:

Determine (22𝑥7𝑥)𝑥sinsind.

  • AsinsinC5𝑥+9𝑥+
  • B5𝑥9𝑥+sinsinC
  • C155𝑥199𝑥+sinsinC
  • D155𝑥+199𝑥+sinsinC
  • E55𝑥+99𝑥+sinsinC

Q5:

Determine (24𝑥7𝑥)𝑥sinsind.

  • A3𝑥11𝑥+sinsinC
  • BsinsinC3𝑥+11𝑥+
  • C133𝑥+11111𝑥+sinsinC
  • D133𝑥11111𝑥+sinsinC
  • E33𝑥1111𝑥+sinsinC

Q6:

Determine 103𝑥3𝑥𝑥tansecd.

  • A5243𝑥+tanC
  • B103𝑥+tanC
  • C5243𝑥+secC
  • D233𝑥+tanC
  • E1033𝑥3𝑥+tansecC

Q7:

Determine 62𝑥3𝑥cosd.

  • A322𝑥+sinC
  • B322𝑥+sinC
  • C124𝑥+sinC
  • D344𝑥+sinC
  • E344𝑥+sinC

Q8:

Determine 27𝑥27𝑥2𝑥sincosd.

  • A𝑥4+7214𝑥+sinC
  • B𝑥47214𝑥+sinC
  • C7𝑥21414𝑥+sinC
  • D𝑥415614𝑥+sinC
  • E𝑥4+15614𝑥+sinC

Q9:

Determine (75𝑥7)𝑥sind.

  • A147𝑥2+49210𝑥+985𝑥+sincosC
  • B147𝑥2+492010𝑥+9855𝑥+sincosC
  • C147𝑥249210𝑥985𝑥+sincosC
  • D147𝑥2492010𝑥9855𝑥+sincosC

Q10:

Determine 75𝑥+7𝑥sind.

  • A21𝑥2+7210𝑥+sinC
  • B21𝑥272010𝑥+sinC
  • C21𝑥27210𝑥+sinC
  • D21𝑥2+72010𝑥+sinC

Q11:

Determine (3𝑥3)(3𝑥3)𝑥coscosd.

  • A9𝑥2922𝑥+sinC
  • B9𝑥2942𝑥+sinC
  • C9𝑥2+942𝑥+sinC
  • D9𝑥2+922𝑥+sinC

Q12:

Determine 5𝑥5𝑥cosd.

  • A5𝑥2252𝑥5+sinC
  • B5𝑥22542𝑥5+sinC
  • C5𝑥22𝑥5+sinC
  • D5𝑥2522𝑥5+sinC

Q13:

Determine (56𝑥+56𝑥)26𝑥+6𝑥𝑥sincostansecd.

  • A25𝑥2+25212𝑥+sinC
  • B25𝑥225212𝑥+sinC
  • C25𝑥2+15012𝑥+sinC
  • D25𝑥2252412𝑥+sinC
  • E25𝑥2+252412𝑥+sinC

Q14:

Determine 6𝑥11𝑥11𝑥coscosd.

  • A611𝑥+cscC
  • B611𝑥+cscC
  • C611𝑥𝑥+cotcscC
  • D611𝑥+tanC

Q15:

Determine 7𝑥47𝑥cosd.

  • A147𝑥2+392𝑥4+49𝑥2+sinsinC
  • B137𝑥47+cosC
  • C49167𝑥47𝑥4+cossinC
  • D147𝑥2+492𝑥4+sinC
  • E147𝑥2+492𝑥4+4916𝑥2+coscosC

Q16:

Determine (55𝑥1)𝑥cosd.

  • A25𝑥+25410𝑥+sinsinC
  • B3𝑥2255𝑥+5410𝑥+sinsinC
  • C25𝑥+25410𝑥+coscosC
  • D252(55𝑥1)+cosC
  • E27𝑥225𝑥+5410𝑥+sinsinC

Q17:

Determine 23𝑥793𝑥9𝑥cossind.

  • A2𝑥97273𝑥+tanC
  • B2𝑥9+793𝑥+tanC
  • C2𝑥9+7273𝑥+tanC
  • D2𝑥9+733𝑥+tanC
  • E2𝑥9793𝑥+tanC

Q18:

Determine 3𝑥39𝑥𝑥coscosd.

  • A3𝑥2+342𝑥139𝑥+sinsinC
  • B3𝑥2+342𝑥139𝑥+coscosC
  • C32𝑥139𝑥+sinsinC
  • D3𝑥2342𝑥9𝑥+sinsinC
  • E32𝑥139𝑥+coscosC

Q19:

Determine (8𝑥2𝑥)𝑥cossecd.

  • A162𝑥+4𝑥+sintanC
  • B32𝑥+82𝑥+2𝑥+sintanC
  • C22𝑥12𝑥+cossecC
  • D32𝑥+162𝑥𝑥+sintanC
  • E13(8𝑥2𝑥)+cossecC

Q20:

Determine 7(4𝑥3)4(4𝑥3)+4𝑥sincosd.

  • A7𝑥4+716(4𝑥3)+sinC
  • B7𝑥74(4𝑥3)+sinC
  • C7𝑥+74(4𝑥3)+sinC
  • D7𝑥4716(4𝑥3)+sinC

Q21:

Determine 859𝑥5𝑥tand.

  • A4𝑥5+72518𝑥+sinC
  • B4𝑥5+4518𝑥+sinC
  • C4𝑥54518𝑥+sinC
  • D4𝑥524518𝑥+sinC
  • E4𝑥5+24518𝑥+sinC

Q22:

Determine 168𝑥𝑥cosd.

  • A8𝑥+1216𝑥+sinC
  • B8𝑥+128𝑥+sinC
  • C1638𝑥+cosC
  • D8𝑥1216𝑥+sinC
  • E8𝑥128𝑥+sinC

Q23:

Determine 3𝑥325𝑥𝑥costand.

  • A342𝑥3105𝑥+sintanC
  • B342𝑥3105𝑥+cossecC
  • C32𝑥355𝑥+cossecC
  • D32𝑥355𝑥+costanC
  • E32𝑥355𝑥+sintanC

Q24:

Determine 32𝑥32𝑥𝑥sincosd.

  • A81𝑥+C
  • B32𝑥32𝑥+sincosC
  • C162𝑥+C
  • D162𝑥+C
  • E81𝑥+C

Q25:

Determine 9𝑥+7𝑥𝑥sincosd.

  • A8𝑥+122𝑥+sinC
  • B8𝑥122𝑥+sinC
  • C73𝑥+3𝑥+sincosC
  • D122𝑥+sinC
  • E21𝑥+27𝑥+sincosC

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