In Exercises 11–14, find the total area of the region between the graph of f and the x-axis.
ƒ(x) = 5 - 5x²/³, -1 ≤ x ≤ 8

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

√x + √y = 1, x = 0, y = 0

Definite Integrals

In Exercises 5–8, express each limit as a definite integral. Then evaluate the integral to find the value of the limit. In each case, P is a partition of the given interval, and the numbers cₖ are chosen from the subintervals of P.

     n

 lim  ∑ (cos(cₖ/2)) ∆xₖ, where P is a partition of [-π, 0]

 ∥P∥→0  k = 1

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

           10           10

Suppose that Σ aₖ = -2 and Σ bₖ = 25. Find the value of

           k = 1          k = 1

  10

a. Σ aₖ/4

  k = 1

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

y² = 4x, y = 4x - 2

Evaluating Definite Integrals

Evaluate the integrals in Exercises 47–68.

∫₋₁¹ (3x² - 4x + 7)dx