Evaluate the integrals in Exercises 47–68.


∫₀ ^π/2 5(sin x)³/² cos x dx

Find the average value of

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a. y = √3x over [0, 3]

Find the areas of the regions enclosed by the curves and lines in Exercises 15–26.

y = x, y = 1/x², x = 2

Evaluate the integrals in Exercises 47–68.

∫₀¹ dr .

∛(7 - 5r)²

Evaluate the integrals in Exercises 37–46.

∫ √t sin(2t³/²)dt

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

Find the areas of the regions enclosed by the curves and lines in Exercises 15–26.

x = 2y², x = 0, y = 3