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Lesson Worksheet: The Fundamental Theorem of Calculus: Evaluating Definite Integrals Mathematics • Higher Education

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In this worksheet, we will practice using the fundamental theorem of calculus to evaluate definite integrals.

Q1:

Determine ο„Έο€Ήβˆ’6π‘₯βˆ’3π‘₯d.

Q2:

Evaluate ο„Έο€Ό45𝑑+34π‘‘βˆ’23π‘‘οˆπ‘‘οŠ§οŠ¦οŠ©οŠ¨d.

  • A5360
  • Bβˆ’140
  • Cβˆ’760
  • D760
  • Eβˆ’5360

Q3:

Evaluate ο„Έ4π‘₯π‘₯d.

Q4:

Let 𝑓(π‘₯)=6π‘₯+1. Evaluate the definite integral of 𝑓 from π‘₯=2 to π‘₯=3.

Q5:

Evaluate ο„Έ|π‘₯βˆ’2|π‘₯οŠͺd.

  • Aβˆ’272
  • B452
  • C292
  • D39

Q6:

Evaluate ο„Έβˆ’2√π‘₯π‘₯οŠͺd.

  • Aβˆ’763
  • B38
  • Cβˆ’76
  • D763
  • Eβˆ’38

Q7:

Determine ο„Έ(4+πœ‹9π‘₯)π‘₯οŠ±οŠ±ο‘½οŽ₯ο‘½οŽ£cosd.

  • A√2πœ‹2+4πœ‹3
  • Bβˆ’14πœ‹9βˆ’βˆš2πœ‹18
  • Cβˆ’4πœ‹3βˆ’βˆš2πœ‹2
  • Dβˆ’4πœ‹9βˆ’βˆš2πœ‹18
  • E√2πœ‹18+4πœ‹9

Q8:

Determine ο„Έ6ο€»πœ‹π‘§4ο‡π‘§οŠ±οŠ«οŠ±οŠ­sind.

  • A24√2πœ‹
  • Bβˆ’24√2πœ‹
  • C4√2πœ‹
  • D24√2

Q9:

Evaluate ο„Έ(2π‘₯βˆ’3𝑒)π‘₯οŠ¨οŠ¦ο—sind.

  • Aβˆ’1βˆ’22+3𝑒cos
  • Bβˆ’22βˆ’3𝑒+3cos
  • Cβˆ’5+22+3𝑒cos
  • Dβˆ’3π‘’βˆ’22+5cos
  • Eβˆ’3𝑒+22+1cos

Q10:

Evaluate ο„Έ4𝑠οŠͺd.

  • Aβˆ’962ln
  • B962ln
  • C192
  • Dβˆ’192
  • E962log

This lesson includes 23 additional questions and 249 additional question variations for subscribers.

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