Worksheet: Definite Integrals of Symmetric Functions

In this worksheet, we will practice evaluating definite integrals for even and odd functions.

Q1:

The function 𝑓 is odd, continuous on [ 1 , 7 ] , and satisfies 𝑓 ( 𝑥 ) 𝑥 = 1 7 7 1 d . Determine 𝑓 ( 𝑥 ) 𝑥 7 1 d .

Q2:

Determine 8 5 𝜃 𝜃 𝜋 𝜋 4 c o s d .

  • A 4 2
  • B 4 2 5
  • C 2 0 2
  • D 4 2 5

Q3:

The function 𝑓 is even, continuous on [ 8 , 8 ] , and satisfies 𝑓 ( 𝑥 ) 𝑥 = 1 9 8 8 d and 𝑓 ( 𝑥 ) 𝑥 = 1 3 4 0 d . Determine 𝑓 ( 𝑥 ) 𝑥 4 8 d .

  • A 3 2
  • B 4 5 2
  • C 2 1 2
  • D 7 2

Q4:

Determine 7 𝑥 5 𝑥 + 5 𝑥 2 2 3 2 d .

Q5:

Determine 9 𝑥 6 𝑥 2 𝑥 + 9 𝑥 1 1 3 2 d .

Q6:

If the even function 𝑓 is continuous over the interval [ 4 , 4 ] , where 𝑓 ( 𝑥 ) 𝑥 = 2 4 0 d , determine the value of 𝑓 ( 𝑥 ) 𝑥 4 4 d .

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