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Worksheet: Evaluating the Definite Integral

Q1:

Evaluate ο„Έ ( 2 π‘₯ βˆ’ 3 𝑒 ) π‘₯ 2 0 π‘₯ s i n d .

  • A βˆ’ 2 2 βˆ’ 3 𝑒 + 3 c o s 2
  • B βˆ’ 3 𝑒 + 2 2 + 1 2 c o s
  • C βˆ’ 1 βˆ’ 2 2 + 3 𝑒 c o s 2
  • D βˆ’ 3 𝑒 βˆ’ 2 2 + 5 2 c o s
  • E βˆ’ 5 + 2 2 + 3 𝑒 c o s 2

Q2:

Determine ο„Έ 2 √ π‘₯ + 6 π‘₯ βˆ’ 2 βˆ’ 5 d .

  • A βˆ’ 4
  • B12
  • C 4 3
  • D4

Q3:

Evaluate ο„Έ | | π‘₯ βˆ’ 4 | | π‘₯ 5 βˆ’ 7 2 d .

  • A342
  • B 3 5 6 3
  • C 2 2 6 3
  • D 3 8 8 3

Q4:

Find ο„Έ π‘˜ π‘₯ + ο„Έ π‘˜ π‘₯ βˆ’ 4 βˆ’ 5 βˆ’ 5 8 d d , given that 𝐾 is a constant.

  • A βˆ’ 6 π‘˜
  • B 1 4 π‘˜
  • C βˆ’ 2 4
  • D βˆ’ 1 2 π‘˜

Q5:

Evaluate ο„Έ βˆ’ 1 1 + π‘₯ π‘₯ √ 3 1 2 d .

  • A 7 πœ‹ 1 2
  • B βˆ’ 7 πœ‹ 1 2
  • C βˆ’ πœ‹ 3
  • D βˆ’ πœ‹ 1 2
  • E πœ‹ 1 2

Q6:

Determine ο„Έ 5 √ βˆ’ π‘₯ + 7 π‘₯ 0 2 d .

  • A βˆ’ 1 0 √ 5 + 1 0 √ 7
  • B βˆ’ 2 0 √ 7 + 2 0 √ 5
  • C βˆ’ 5 0 √ 7 + 5 0 √ 5
  • D βˆ’ 1 0 √ 7 + 1 0 √ 5