Lesson Worksheet: Definite Integrals: The Power Rule Mathematics

In this worksheet, we will practice evaluating definite integrals using the power rule.


Evaluate 𝑥𝑥d.

  • A645
  • B645
  • C6410
  • D6410
  • E0


Evaluate 2𝑥𝑥d.

  • A763
  • B38
  • C76
  • D763
  • E38


Evaluate 45𝑡+34𝑡23𝑡𝑡d.

  • A5360
  • B140
  • C760
  • D760
  • E5360


Determine 3𝑥3𝑥+1𝑥d.

  • A486
  • B32
  • C54
  • D9


Evaluate 45𝑥𝑥𝑥d.

  • A6
  • B4373
  • C4373
  • D54
  • E54


Evaluate 2𝑥3𝑥𝑥d.

  • A1,86815
  • B0
  • C1,8685
  • D1,86815
  • E1,8685


Given that (3𝑥+𝑎)𝑥=3𝑎d for some constant 𝑎, find the value of 𝑎.

  • A𝑎=9.5
  • B𝑎=1
  • C𝑎=19
  • D𝑎=19
  • E𝑎=9.5


Given that 4𝑥𝑥=𝑎+𝑏2d for some constants 𝑎 and 𝑏, find the values of 𝑎 and 𝑏.

  • A𝑎=16, 𝑏=8
  • B𝑎=4, 𝑏=2
  • C𝑎=4, 𝑏=2
  • D𝑎=16, 𝑏=8
  • E𝑎=16, 𝑏=8


Given that 2𝑥𝑥=9d, find the value of 𝑘 given that it is greater than 1.


A car is traveling along a road in a straight line and its velocity after 𝑡 seconds is given by 𝑣=𝑡+𝑡+10ms. The displacement 𝑠 of the car in meters after 10 seconds is given by 𝑡+𝑡+10𝑡d. Find the displacement of the car after 10 seconds.

  • A1,4503 meters
  • B5753 meters
  • C2,9003 meters
  • D7253 meters
  • E1,1503 meters

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