If ∫²₋₂ 3ƒ(x) dx = 12, ∫⁵₋₂ ƒ(x) dx = 6, and ∫⁵₋₂ g(x) dx = 2, find the value of each of the following.


d. ∫⁵₋₂ (-πg(x)) dx

Evaluate the integrals in Exercises 1–22.

∫₀^(π/6) 3cos⁵(3x) dx

Evaluating Definite Integrals

Evaluate the integrals in Exercises 47–68.

∫₋₁¹ (3x² - 4x + 7)dx

Evaluate the integrals in Exercises 47–68.

∫₁² 4 dv

v²

If ∫²₋₂ 3ƒ(x) dx = 12, ∫⁵₋₂ ƒ(x) dx = 6, and ∫⁵₋₂ g(x) dx = 2, find the value of each of the following.

a. ∫²₋₂ ƒ(x) dx

If ∫²₋₂ 3ƒ(x) dx = 12, ∫⁵₋₂ ƒ(x) dx = 6, and ∫⁵₋₂ g(x) dx = 2, find the value of each of the following.

e. ∫⁵₋₂ ( ƒ(x) + g(x) ) dx

5

If ∫₀² ƒ(x) dx = π, ∫₀² 7g(x) dx = 7, and ∫₀¹ g(x) dx = 2, find the value of each of the following.

b. ∫₁² g(x) dx

If ∫₀² ƒ(x) dx = π, ∫₀² 7g(x) dx = 7, and ∫₀¹ g(x) dx = 2, find the value of each of the following.

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d. ∫₀² √2ƒ(x) dx

Evaluate the integrals in Exercises 23–32.

∫₀^π √(1 - cos(2x)) dx