Worksheet: Integration by Parts for Definite Integrals

In this worksheet, we will practice using integration by parts or partial integration for definite integrals to find the integral of a product of functions in terms of the integral of their derivative and anti derivative.

Q1:

Use integration by parts to find the exact value of 𝑥 2 𝑥 𝑥 𝜋 / 4 0 2 s i n d .

  • A 1 4 𝜋 8
  • B 𝜋 4 1 4
  • C 1 4 𝜋 4
  • D 𝜋 8 1 4
  • E 𝜋 8 + 1 4

Q2:

Evaluate 𝑥 𝑒 𝑥 d .

  • A 𝑒 + 2
  • B 2 3 𝑒
  • C 𝑒 1
  • D 𝑒 2
  • E 1 𝑒

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