- 9-1.1: Find the approximate volume of the solid in Figure 9-1a by numerica...
- 9-1.2: Let f(x) = x sin x. Use the derivative of a product formula to find...
- 9-1.3: Multiply both sides of the equation for (x) in by dx. Then integrat...
- 9-1.4: The integral x cos x dx should be one term in the equation of 3. Us...
- 9-1.5: Use the result of to find the exact volume of the solid in Figure 9...
- 9-1.6: Find a decimal approximation for the exact volume in 5. How close d...
- 9-1.7: The technique of this exercise is called integration by parts. Why ...
Solutions for Chapter 9-1: Introduction to the Integral of a Product of Two Functions
Full solutions for Calculus: Concepts and Applications | 2nd Edition
Solutions for Chapter 9-1: Introduction to the Integral of a Product of Two FunctionsGet Full Solutions
Components of a vector
See Component form of a vector.
Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)
The function y = cos x
Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2 - x 1, y2 - y19>
Connected subset of the real number line with at least two points, p. 4.
See Polynomial function in x.
Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.
See Numerical derivative of ƒ at x = a.
Two vectors u and v with u x v = 0.
Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data
Ratio change in y/change in x
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically
A set of points in Cartesian space equally distant from a fixed point called the center.
a - b = a + (-b)
Vertices of an ellipse
The points where the ellipse intersects its focal axis.
A point that lies on both the graph and the x-axis,.