 7.1: Evaluate the integral.
 7.2: Evaluate the integral.
 7.3: Evaluate the integral.
 7.4: Evaluate the integral.
 7.5: Evaluate the integral.
 7.6: Evaluate the integral.
 7.7: Evaluate the integral.
 7.8: Evaluate the integral.
 7.9: Evaluate the integral.
 7.10: Evaluate the integral.
 7.11: Evaluate the integral.
 7.12: Evaluate the integral.
 7.13: Evaluate the integral.
 7.14: Evaluate the integral.
 7.15: Evaluate the integral.
 7.16: Evaluate the integral.
 7.17: Evaluate the integral.
 7.18: Evaluate the integral.
 7.19: Evaluate the integral.
 7.20: Evaluate the integral.
 7.21: Evaluate the integral.
 7.22: Evaluate the integral.
 7.23: Evaluate the integral.
 7.24: Evaluate the integral.
 7.25: Evaluate the integral.
 7.26: Evaluate the integral.
 7.27: Evaluate the integral.
 7.28: Evaluate the integral.
 7.29: Evaluate the integral.
 7.30: Evaluate the integral.
 7.31: Evaluate the integral.
 7.32: Evaluate the integral.
 7.33: Evaluate the integral.
 7.34: Evaluate the integral.
 7.35: Evaluate the integral.
 7.36: Evaluate the integral.
 7.37: Evaluate the integral.
 7.38: Evaluate the integral.
 7.39: Evaluate the integral.
 7.40: Evaluate the integral.
 7.41: Evaluate the integral or show that it is divergent.
 7.42: Evaluate the integral or show that it is divergent.
 7.43: Evaluate the integral or show that it is divergent.
 7.44: Evaluate the integral or show that it is divergent.
 7.45: Evaluate the integral or show that it is divergent.
 7.46: Evaluate the integral or show that it is divergent.
 7.47: Evaluate the integral or show that it is divergent.
 7.48: Evaluate the integral or show that it is divergent.
 7.49: Evaluate the integral or show that it is divergent.
 7.50: Evaluate the integral or show that it is divergent.
 7.51: Evaluate the indefinite integral. Illustrate and check that your an...
 7.52: Evaluate the indefinite integral. Illustrate and check that your an...
 7.53: Graph the function and use the graph to guess the value of the inte...
 7.54: (a) How would you evaluate by hand? (Dont actually carry out the in...
 7.55: Use the Table of Integrals on the Reference Pages to evaluate the i...
 7.56: Use the Table of Integrals on the Reference Pages to evaluate the i...
 7.57: Use the Table of Integrals on the Reference Pages to evaluate the i...
 7.58: Use the Table of Integrals on the Reference Pages to evaluate the i...
 7.59: Verify Formula 33 in the Table of Integrals (a) by differentiation ...
 7.60: Verify Formula 62 in the Table of Integrals.
 7.61: Is it possible to find a number such that is convergent?
 7.62: For what values of is convergent? Evaluate the integral for those v...
 7.63: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpso...
 7.64: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpso...
 7.65: Estimate the errors involved in Exercise 63, parts (a) and (b). How...
 7.66: Use Simpsons Rule with to estimate the area under the curve from to .
 7.67: The speedometer reading (v) on a car was observed at 1minute inter...
 7.68: A population of honeybees increased at a rate of r(t) bees per week...
 7.69: (a) If , use a graph to find an upper bound for . (b) Use Simpsons ...
 7.70: Suppose you are asked to estimate the volume of a football. You mea...
 7.71: Use the Comparison Theorem to determine whether the integral is con...
 7.72: Find the area of the region bounded by the hyperbola and the line
 7.73: Find the area bounded by the curves and
 7.74: Find the area of the region bounded by the curves
 7.75: The region under the curve , is rotated about the axis. Find the v...
 7.76: The region in Exercise 75 is rotated about the yaxis. Find the vol...
 7.77: If is continuous on and , show that
 7.78: We can extend our definition of average value of a continuous funct...
 7.79: Use the substitution to show that
 7.80: The magnitude of the repulsive force between two point charges with...
Solutions for Chapter 7: Calculus, 7th Edition
Full solutions for Calculus,  7th Edition
ISBN: 9780538497817
Solutions for Chapter 7
Get Full SolutionsChapter 7 includes 80 full stepbystep solutions. Calculus, was written by and is associated to the ISBN: 9780538497817. This textbook survival guide was created for the textbook: Calculus,, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Since 80 problems in chapter 7 have been answered, more than 7927 students have viewed full stepbystep solutions from this chapter.

Acute triangle
A triangle in which all angles measure less than 90°

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

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Interquartile range
The difference between the third quartile and the first quartile.

Line of travel
The path along which an object travels

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Logarithmic regression
See Natural logarithmic regression

Nappe
See Right circular cone.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Randomization
The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Scalar
A real number.

Speed
The magnitude of the velocity vector, given by distance/time.

Symmetric property of equality
If a = b, then b = a

xaxis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.

xyplane
The points x, y, 0 in Cartesian space.