 5.2.1: Evaluate the Riemann sum for , , with six subintervals, taking the ...
 5.2.2: If , , evaluate the Riemann sum with , taking the sample points to ...
 5.2.3: If , , nd the Riemann sum with correct to six decimal places, takin...
 5.2.4: (a) Find the Riemann sum for , , with six terms, taking the sample ...
 5.2.5: The graph of a function is given. Estimate using four subintervals ...
 5.2.6: The graph of is shown. Estimate with six subintervals using (a) rig...
 5.2.7: A table of values of an increasing function is shown. Use the table...
 5.2.8: The table gives the values of a function obtained from an experimen...
 5.2.9: Use the Midpoint Rule with the given value of to approximate the in...
 5.2.10: Use the Midpoint Rule with the given value of to approximate the in...
 5.2.11: Use the Midpoint Rule with the given value of to approximate the in...
 5.2.12: Use the Midpoint Rule with the given value of to approximate the in...
 5.2.13: If you have a CAS that evaluates midpoint approximations and graphs...
 5.2.14: With a programmable calculator or computer (see the instructions fo...
 5.2.15: Use a calculator or computer to make a table of values of right Rie...
 5.2.16: Use a calculator or computer to make a table of values of left and ...
 5.2.17: Express the limit as a denite integral on the given interval.
 5.2.18: Express the limit as a denite integral on the given interval.
 5.2.19: Express the limit as a denite integral on the given interval.
 5.2.20: Express the limit as a denite integral on the given interval.
 5.2.21: Use the form of the denition of the integral given in Theorem 4 to ...
 5.2.22: Use the form of the denition of the integral given in Theorem 4 to ...
 5.2.23: Use the form of the denition of the integral given in Theorem 4 to ...
 5.2.24: Use the form of the denition of the integral given in Theorem 4 to ...
 5.2.25: Use the form of the denition of the integral given in Theorem 4 to ...
 5.2.26: (a) Find an approximation to the integral using a Riemann sum with ...
 5.2.27: Express the integral as a limit of Riemann sums. Do not evaluate th...
 5.2.28: Express the integral as a limit of Riemann sums. Do not evaluate th...
 5.2.29: Express the integral as a limit of sums. Then evaluate, using a com...
 5.2.30: Express the integral as a limit of sums. Then evaluate, using a com...
 5.2.31: The graph of is shown. Evaluate each integral by interpreting it in...
 5.2.32: The graph of t consists of two straight lines and a semicircle. Use...
 5.2.33: Evaluate the integral by interpreting it in terms of areas.
 5.2.34: Evaluate the integral by interpreting it in terms of areas.
 5.2.35: Evaluate the integral by interpreting it in terms of areas.
 5.2.36: Evaluate the integral by interpreting it in terms of areas.
 5.2.37: Evaluate the integral by interpreting it in terms of areas.
 5.2.38: Evaluate the integral by interpreting it in terms of areas.
 5.2.39: Evaluate .
 5.2.40: Given that , what is?
 5.2.41: Write as a single integral in the form :y2 2 fxdx y5 2 fxdx y1 2 fxdx
 5.2.42: If and , nd .
 5.2.43: If and , nd .
 5.2.44: Find iffx 3 for x 3 x for x 3
 5.2.45: Use the result of Example 3 to evaluate .
 5.2.46: Use the properties of integrals and the result of Example 3 to eval...
 5.2.47: For the function whose graph is shown, list the following quantitie...
 5.2.48: If , where is the function whose graph is given, which of the follo...
 5.2.49: Each of the regions , , and bounded by the graph of and the axis h...
 5.2.50: Suppose has absolute minimum value and absolute maximum value . Bet...
 5.2.51: Use the properties of integrals to verify that2y1 1 s1 x2 dx2s2
 5.2.52: Use Property 8 to estimate the value of the integraly2 0 1 1 x2 dx
 5.2.53: Express the limit as a denite integral. [Hint: Consider
 5.2.54: Express the limit as a denite integral.lim nl 1 n n i1 1 1 in2
 5.2.55: Let if is any rational number and if is any irrational number. Show...
 5.2.56: Let and if . Show that is not integrable on . [Hint: Show that the ...
Solutions for Chapter 5.2: THE DEFINITE INTEGRAL
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series)  4th Edition
ISBN: 9780495559726
Solutions for Chapter 5.2: THE DEFINITE INTEGRAL
Get Full SolutionsSingle Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by and is associated to the ISBN: 9780495559726. Chapter 5.2: THE DEFINITE INTEGRAL includes 56 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: Concepts and Contexts (Stewart's Calculus Series), edition: 4. Since 56 problems in chapter 5.2: THE DEFINITE INTEGRAL have been answered, more than 20713 students have viewed full stepbystep solutions from this chapter.

Conversion factor
A ratio equal to 1, used for unit conversion

Directed line segment
See Arrow.

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

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

nth root
See Principal nth root

nth root of unity
A complex number v such that vn = 1

Order of an m x n matrix
The order of an m x n matrix is m x n.

Parameter interval
See Parametric equations.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Quartic function
A degree 4 polynomial function.

Quartile
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.

Right triangle
A triangle with a 90° angle.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Rose curve
A graph of a polar equation or r = a cos nu.

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

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is