 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 ( ) on a car was observed at 1minute inter...
 7.68: A population of honeybees increased at a rate of bees per week, whe...
 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
 7.73: Find the area bounded by the curves and between and .
 7.74: Find the area of the region bounded by the curves , , and .
 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 axis. Find the volu...
 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: Single Variable Calculus 7th Edition
Full solutions for Single Variable Calculus  7th Edition
ISBN: 9780538497831
Solutions for Chapter 7
Get Full SolutionsChapter 7 includes 80 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 80 problems in chapter 7 have been answered, more than 5201 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Single Variable Calculus, edition: 7. Single Variable Calculus was written by and is associated to the ISBN: 9780538497831.

Average velocity
The change in position divided by the change in time.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Difference identity
An identity involving a trigonometric function of u  v

Equal matrices
Matrices that have the same order and equal corresponding elements.

Equivalent arrows
Arrows that have the same magnitude and direction.

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Linear regression
A procedure for finding the straight line that is the best fit for the data

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Principle of mathematical induction
A principle related to mathematical induction.

Proportional
See Power function

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Vertices of an ellipse
The points where the ellipse intersects its focal axis.

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.