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Lesson Worksheet: Indefinite Integrals: The Power Rule Mathematics • 12th Grade

In this worksheet, we will practice finding the indefinite integrals of polynomials and general power functions using the power rule for integration.

Q1:

Determine −𝑥𝑥d.

  • A−10𝑥+C
  • B−𝑥9+C
  • C−𝑥10+C
  • D−𝑥8+C
  • E−9𝑥+C

Q2:

Determine −27𝑥𝑥d.

  • A−27𝑥+C
  • B263𝑥+C
  • C128𝑥+C
  • D135𝑥+C
  • E167𝑥+C

Q3:

Determine 7√𝑥𝑥d.

  • A7√𝑥+C
  • B145√𝑥+C
  • C143√𝑥+C
  • D70√𝑥+C
  • E14√𝑥+C

Q4:

Determine 6√𝑥𝑥d.

  • A−48𝑥+C
  • B6𝑥+C
  • C−163𝑥+C
  • D487𝑥+C
  • E214𝑥+C

Q5:

Determine 25𝑥−65𝑥+36𝑥d.

  • A25𝑥−65𝑥+36𝑥+C
  • B25𝑥+C
  • C252𝑥−65𝑥+36𝑥+C
  • D75𝑥−130𝑥+36𝑥+C
  • E253𝑥−652𝑥+36𝑥+C

Q6:

Determine (𝑥+4)𝑥−4𝑥+16𝑥d.

  • A𝑥2+64𝑥+C
  • B4𝑥+64𝑥+C
  • C𝑥3+64𝑥+C
  • D𝑥4+64𝑥+C

Q7:

Determine 𝑥−225𝑥−15𝑥d.

  • A𝑥2+15𝑥+C
  • B16𝑥+C
  • C𝑥2+C
  • D𝑥2−15𝑥+C

Q8:

Determine −8+89𝑥+75𝑥𝑥d.

  • A−8𝑥−49𝑥−730𝑥+C
  • B−8𝑥−89𝑥−725𝑥+C
  • C−8𝑥−89𝑥−7𝑥+C
  • D−8𝑥−827𝑥−15𝑥+C

Q9:

Determine −√𝑥+8+9𝑥𝑥d.

  • A−2√𝑥−9𝑥+C
  • B8𝑥−2√𝑥+9𝑥+C
  • C−𝑥+9𝑥+C
  • D8𝑥−2√𝑥3−9𝑥+C

Q10:

Determine 36𝑥−49√𝑥(6𝑥+7)𝑥d.

  • A6𝑥−7𝑥+C
  • B48𝑥7+56𝑥+C
  • C16𝑥5−8𝑥+C
  • D45𝑥4−49𝑥8+C

This lesson includes 129 additional questions and 603 additional question variations for subscribers.

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