 5.8.1: Find b such that b 1 dx x is equal to (a) ln 3. (b) 3.
 5.8.2: Find b such that b 0 dx 1 + x2 = 3 .
 5.8.3: Which integral should be evaluated using substitution? (a) 9 dx 1 +...
 5.8.4: Which relation between x and u yields 16 + x2 = 4 1 + u2?
 5.8.5: In Exercises 110, evaluate the definite integral.12 2 dt 3t + 4
 5.8.6: In Exercises 110, evaluate the definite integral.e3 e dt t ln t
 5.8.7: In Exercises 110, evaluate the definite integral.3 1 dx x2 + 1
 5.8.8: In Exercises 110, evaluate the definite integral.7 2 x dx x2 + 1
 5.8.9: In Exercises 110, evaluate the definite integral.1/2 0 dx 1 x2
 5.8.10: In Exercises 110, evaluate the definite integral.2/ 3 2 dx x x2 1
 5.8.11: Use the substitution u = x/3 to prove dx 9 + x2 = 1 3 tan1 x 3 + C
 5.8.12: Use the substitution u = 2x to evaluate dx 4x2 + 1
 5.8.13: In Exercises 1332, calculate the integral. 13. 3 0 dx x2 + 3
 5.8.14: In Exercises 1332, calculate the integral.4 0 dt 4t2 + 9
 5.8.15: In Exercises 1332, calculate the integral.dt 1 16t2
 5.8.16: In Exercises 1332, calculate the integral.1/5 1/5 dx 4 25x2
 5.8.17: In Exercises 1332, calculate the integral.dt 5 3t2
 5.8.18: In Exercises 1332, calculate the integral.1/2 1/ 2 2 dx x 16x2 1
 5.8.19: In Exercises 1332, calculate the integral.dx x 12x2 3
 5.8.20: In Exercises 1332, calculate the integral.x dx x4 + 1
 5.8.21: In Exercises 1332, calculate the integral.dx x x4 1
 5.8.22: In Exercises 1332, calculate the integral.0 1/2 (x + 1)dx 1 x2
 5.8.23: In Exercises 1332, calculate the integral.0 ln 2 ex dx 1 + e2x
 5.8.24: In Exercises 1332, calculate the integral.ln(cos1 x) dx (cos1 x) 1 x2
 5.8.25: In Exercises 1332, calculate the integral.tan1 x dx 1 + x2
 5.8.26: In Exercises 1332, calculate the integral.3 1 dx (tan1 x)(1 + x2)
 5.8.27: In Exercises 1332, calculate the integral.1 0 3x dx
 5.8.28: In Exercises 1332, calculate the integral.1 0 3x dx
 5.8.29: In Exercises 1332, calculate the integral.log4(3) 0 4x dx
 5.8.30: In Exercises 1332, calculate the integral.1 0 t 5t2 dt
 5.8.31: In Exercises 1332, calculate the integral.9x sin(9x )dx
 5.8.32: In Exercises 1332, calculate the integral.dx 52x 1
 5.8.33: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.34: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.35: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.36: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.37: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.38: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.39: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.40: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.41: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.42: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.43: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.44: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.45: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.46: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.47: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.48: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.49: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.50: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.51: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.52: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.53: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.54: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.55: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.56: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.57: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.58: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.59: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.60: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.61: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.62: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.63: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.64: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.65: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.66: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.67: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.68: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.69: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.70: In Exercises 3370, evaluate the integral using the methods covered ...
 5.8.71: Use Figure 4 to prove x 0 1 t2 dt = 1 2 x 1 x2 + 1 2 sin1 x
 5.8.72: Use the substitution u = tan x to evaluate dx 1 + sin2 x Hint: Show...
 5.8.73: Prove sin1 t dt = 1 t2 + t sin1 t
 5.8.74: (a) Verify for r = 0: T 0 tert dt = erT (rT 1) + 1 r2 6 Hint: For f...
 5.8.75: Recall that if f (t) g(t) for t 0, then for all x 0, x 0 f (t) dt x...
 5.8.76: Generalize Exercise 75; that is, use induction (if you are familiar...
 5.8.77: Use Exercise 75 to show that ex /x2 x/6 and conclude that lim x ex ...
 5.8.78: Exercises 7880 develop an elegant approach to the exponential and l...
 5.8.79: Exercises 7880 develop an elegant approach to the exponential and l...
 5.8.80: Exercises 7880 develop an elegant approach to the exponential and l...
 5.8.81: The formula xn dx = xn+1 n + 1 + C is valid for n = 1. Show that th...
 5.8.82: The integral inside the limit on the left in Exercise 81 is equal t...
 5.8.83: (a) Explain why the shaded region in Figure 5 has area ln a 0 ey dy...
Solutions for Chapter 5.8: Further Transcendental Functions
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 5.8: Further Transcendental Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.8: Further Transcendental Functions includes 83 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Since 83 problems in chapter 5.8: Further Transcendental Functions have been answered, more than 44531 students have viewed full stepbystep solutions from this chapter.

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Completing the square
A method of adding a constant to an expression in order to form a perfect square

DMS measure
The measure of an angle in degrees, minutes, and seconds

Exponent
See nth power of a.

Fibonacci numbers
The terms of the Fibonacci sequence.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

First quartile
See Quartile.

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Inverse cosecant function
The function y = csc1 x

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Radicand
See Radical.

Right triangle
A triangle with a 90° angle.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.