 7.8.1: Explain why each of the following integrals is improper. (a) y 2 1 ...
 7.8.2: Which of the following integrals are improper? Why? (a) y y4 0 tan ...
 7.8.3: Find the area under the curve y 1yx 3 from x 1 to x t and evaluate ...
 7.8.4: (a) Graph the functions fsxd 1yx 1.1 and tsxd 1yx 0.9 in the viewin...
 7.8.5: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.6: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.7: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.8: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.9: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.10: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.11: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.12: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.13: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.14: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.15: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.16: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.17: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.18: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.19: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.20: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.21: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.22: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.23: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.24: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.25: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.26: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.27: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.28: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.29: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.30: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.31: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.32: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.33: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.34: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.35: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.36: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.37: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.38: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.39: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.40: 540 Determine whether each integral is convergent or divergent. Eva...
 7.8.41: 4146 Sketch the region and find its area (if the area is finite).
 7.8.42: 4146 Sketch the region and find its area (if the area is finite).
 7.8.43: 4146 Sketch the region and find its area (if the area is finite).
 7.8.44: 4146 Sketch the region and find its area (if the area is finite).
 7.8.45: 4146 Sketch the region and find its area (if the area is finite).
 7.8.46: 4146 Sketch the region and find its area (if the area is finite).
 7.8.47: (a) If tsxd ssin2 xdyx 2 , use your calculator or computer to make ...
 7.8.48: (a) If tsxd ssin2 xdyx 2 , use your calculator or computer to make ...
 7.8.49: 4954 Use the Comparison Theorem to determine whether the integral i...
 7.8.50: 4954 Use the Comparison Theorem to determine whether the integral i...
 7.8.51: 4954 Use the Comparison Theorem to determine whether the integral i...
 7.8.52: 4954 Use the Comparison Theorem to determine whether the integral i...
 7.8.53: 4954 Use the Comparison Theorem to determine whether the integral i...
 7.8.54: 4954 Use the Comparison Theorem to determine whether the integral i...
 7.8.55: The integral y ` 0 1 sx s1 1 xd d
 7.8.56: Evaluate y ` 2 1 xsx 2 2 4 dx by the same method as in Exercise 55
 7.8.57: 5759 Find the values of p for which the integral converges and eval...
 7.8.58: 5759 Find the values of p for which the integral converges and eval...
 7.8.59: 5759 Find the values of p for which the integral converges and eval...
 7.8.60: (a) Evaluate the integral y ` 0 x n e2x dx for n 0, 1, 2, and 3. (b...
 7.8.61: (a) Show that y` 2` x dx is divergent. (b) Show that lim tl` y t 2t...
 7.8.62: The average speed of molecules in an ideal gas is v 4 s S M 2RT D 3...
 7.8.63: We know from Example 1 that the region 5 hsx, yd  x > 1, 0 < y < 1...
 7.8.64: Use the information and data in Exercise 6.4.33 to find the work re...
 7.8.65: Find the escape velocity v0 that is needed to propel a rocket of ma...
 7.8.66: Astronomers use a technique called stellar stereography to determin...
 7.8.67: A manufacturer of lightbulbs wants to produce bulbs that last about...
 7.8.68: As we saw in Section 3.8, a radioactive substance decays exponentia...
 7.8.69: In a study of the spread of illicit drug use from an enthusiastic u...
 7.8.70: Dialysis treatment removes urea and other waste products from a pat...
 7.8.71: Determine how large the number a has to be so that y ` a 1 x 2 1 1 ...
 7.8.72: Determine how large the number a has to be so that y ` a 1 x 2 1 1 ...
 7.8.73: If fstd is continuous for t > 0, the Laplace transform of f is the ...
 7.8.74: Show that if 0 < fstd < Me at for t > 0, where M and a are constant...
 7.8.75: Suppose that 0 < fstd < Me at and 0 < f9std < Ke at for t > 0, wher...
 7.8.76: If y` 2` fsxd dx is convergent and a and b are real numbers, show t...
 7.8.77: Show that y ` 0 x 2 e2x 2 dx 1 2 y ` 0 e2x 2 dx
 7.8.78: Show that y` 0 e2x 2 dx y 1 0 s2ln y dy by interpreting the integra...
 7.8.79: Find the value of the constant C for which the integral y ` 0 S 1 s...
 7.8.80: Find the value of the constant C for which the integral y ` 0 S x x...
 7.8.81: Suppose f is continuous on f0, `d and limxl` fsxd 1. Is it possible...
 7.8.82: Show that if a . 21 and b . a 1 1, then the following integral is c...
Solutions for Chapter 7.8: Improper Integrals
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 7.8: Improper Integrals
Get Full SolutionsSingle Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. Since 82 problems in chapter 7.8: Improper Integrals have been answered, more than 38118 students have viewed full stepbystep solutions from this chapter. Chapter 7.8: Improper Integrals includes 82 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8.

Additive inverse of a real number
The opposite of b , or b

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Branches
The two separate curves that make up a hyperbola

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Cycloid
The graph of the parametric equations

Distributive property
a(b + c) = ab + ac and related properties

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Inverse secant function
The function y = sec1 x

Logistic regression
A procedure for fitting a logistic curve to a set of data

Modified boxplot
A boxplot with the outliers removed.

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

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

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Seconddegree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.