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Problem 5.PE.77
In Exercises 75–78, find dy/dx.
y = ∫(from x to 1) (6/(3 + t^4))dt
Problem 5.PE.17
Find the areas of the regions enclosed by the curves and lines in Exercises 15–26.
√x + √y = 1, x = 0, y = 0
Problem 5.PE.7
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
Problem 5.PE.10b
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
Problem 5.PE.13
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
Problem 5.PE.3a
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
Problem 5.PE.21
Find the areas of the regions enclosed by the curves and lines in Exercises 15–26.
y² = 4x, y = 4x - 2
Problem 5.PE.47
Evaluating Definite Integrals
Evaluate the integrals in Exercises 47–68.
∫₋₁¹ (3x² - 4x + 7)dx
Problem 5.PE.39
Evaluate the integrals in Exercises 37–46.
∫(2θ + 1 + 2 cos (2θ + 1))dθ
Problem 5.PE.70a
Find the average value of
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a. y = √3x over [0, 3]
