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04:567–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.
37. ∫ dx / √(x² + 10x), x >
7–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.
11. ∫ 3u / (2u + 7) du
{Use of Tech} Using the integral of sec³u By reduction formula 4 in Section 8.3,
∫sec³u du = 1/2 (sec u tan u + ln |sec u + tan u|) + C
Graph the following functions and find the area under the curve on the given interval.
f(x) = 1/(x√(x² - 36)), [12/√3 , 12]
92–98. Evaluate the following integrals.
97. ∫ tan⁻¹(∛x) dx
49–52. {Use of Tech} Simpson’s Rule
Apply Simpson’s Rule to the following integrals. It is easiest to obtain the Simpson’s Rule approximations from the Trapezoid Rule approximations, as in Example 8. Make a table similar to Table 8.8 showing the approximations and errors for n = 4, 8, 16, and 32. The exact values of the integrals are given for computing the error.
51. ∫(from 0 to π) e⁻ᵗ sin(t) dt = ½(e⁻ᵖⁱ + 1)
7-56. Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.
44. ∫ 1/√(16 + 4x²) dx
