Evaluate the integrals in Exercises 37–46.


∫ √t sin(2t³/²)dt

Find the average value of

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a. y = √3x over [0, 3]

Evaluate the integrals in Exercises 47–68.

∫₀¹ dr .

∛(7 - 5r)²

Evaluate the integrals in Exercises 47–68.

∫₀ ^π/2 5(sin x)³/² cos 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.

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

Find the extreme values of ƒ(x) = x³ - 3x², and find the area of the region enclosed by the graph of ƒ and the x-axis.