뒤로
문제 8.1.32
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫₋₁¹ (√(1 + x²) sin x) dx
문제 8.6.2
Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.
∫ dx / (x √(x + 4))
문제 8.8.34
The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.
∫₀^∞ dx / [(x + 1)(x² + 1)]
문제 8.8.62
In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.
∫ from 2 to ∞ of ((1 / ln x) dx)
문제 8.8.4
The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.
∫₀⁴ dx / √(4 − x)
문제 8.6.8
Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.
∫ dx / (x² √(4x - 9))
문제 8.3.40
Evaluate the integrals in Exercises 33–52.
∫ eˣ sec³(eˣ) dx
문제 8.1.12
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫₋₁³ (4x² - 7) / (2x + 3) dx
문제 8.1.48
Arc length: Find the length of the curve y = ln(sec x), 0 ≤ x ≤ π/4.
문제 8.3.52
Evaluate the integrals in Exercises 33–52.
∫ cot³(t) csc⁴(t) dt
문제 8.3.48
Evaluate the integrals in Exercises 33–52.
∫ cot⁶(2x) dx
문제 8.5.75
[Technology Exercise] 75. Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant bounded by the x-axis, the curve y = arctan(x), and the line x = √3.
문제 8.1.30
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫ 3 sinh(x/2 + ln 5) dx
문제 8.3.24
Evaluate the integrals in Exercises 23–32.
∫₀^π √(1 - cos(2x)) dx
문제 8.2.76
Use integration by parts to obtain the formula ∫ √(1 - x²) dx = (1/2) x √(1 - x²) + (1/2) ∫ 1 / √(1 - x²) dx.
문제 8.1.4
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫ (1 / (cos² x tan x)) dx from π/3 to π/4
문제 8.4.8
Evaluate the integrals in Exercises 1–14.
∫ √(1 - 9t²) dt
문제 8.5.6
Expand the quotients in Exercises 1–8 by partial fractions.
z / (z³ - z² - 6z)
문제 8.8.10
The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.
∫₋∞² (2 dx) / (x² + 4)
문제 8.1.14
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫ (csc t sin 3t dt)
문제 8.5.58
Use any method to evaluate the integrals in Exercises 55–66.
∫ 2^x / (2²x + 2^x - 2) dx
문제 8.1.38
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫ (dθ / cos θ - 1)
문제 8.2.46
Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.
∫ √x e√x dx
문제 8.8.74
In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.
∫₋₂¹ (1 / x⁴) dx
문제 8.1.18
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫ (2^(√y) dy) / 2√y
문제 8.3.18
Evaluate the integrals in Exercises 1–22.
∫₀^π 8cos⁴(2πx) dx
문제 8.1.2
The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.
∫ (x² / (x² + 1)) dx
문제 8.5.40
Evaluate the integrals in Exercises 39–54.
∫ (e⁴t + 2e²t - e^t) / (e²t + 1) dt
문제 8.5.56
Use any method to evaluate the integrals in Exercises 55–66.
∫ (x + 2) / (x³ - 2x² - 3x) dx
문제 8.8.86
Exercises 83–86 are about the infinite region in the first quadrant between the curve y = e^(-x) and the x-axis.
86. Find the volume of the solid generated by revolving the region about the x-axis.