 5.1: In Exercises 14, refer to the function f whose graph is shown in Fi...
 5.2: In Exercises 14, refer to the function f whose graph is shown in Fi...
 5.3: In Exercises 14, refer to the function f whose graph is shown in Fi...
 5.4: In Exercises 14, refer to the function f whose graph is shown in Fi...
 5.5: In Exercises 58, let f (x) = x2 + 3x. Calculate R6, M6, and L6 for ...
 5.6: In Exercises 58, let f (x) = x2 + 3x. Use FTC I to evaluate A(x) = ...
 5.7: In Exercises 58, let f (x) = x2 + 3x. Find a formula for RN for f o...
 5.8: In Exercises 58, let f (x) = x2 + 3x. Find a formula for LN for f o...
 5.9: Calculate R5, M5, and L5 for f (x) = (x2 + 1)1 on the interval [0, 1].
 5.10: Let RN be the Nth rightendpoint approximation for f (x) = x3 on [0...
 5.11: Which approximation to the area is represented by the shaded rectan...
 5.12: Calculate any two Riemann sums for f (x) = x2 on the interval [2, 5...
 5.13: In Exercises 1316, express the limit as an integral (or multiple of...
 5.14: In Exercises 1316, express the limit as an integral (or multiple of...
 5.15: In Exercises 1316, express the limit as an integral (or multiple of...
 5.16: In Exercises 1316, express the limit as an integral (or multiple of...
 5.17: In Exercises 1730, calculate the indefinite integral. 17. 4x3 2x2 dx
 5.18: In Exercises 1730, calculate the indefinite integral.x9/4 dx
 5.19: In Exercises 1730, calculate the indefinite integral.]sin( 8)d
 5.20: In Exercises 1730, calculate the indefinite integral.cos(5 7)d
 5.21: In Exercises 1730, calculate the indefinite integral.(4t 3 12t 4)dt
 5.22: In Exercises 1730, calculate the indefinite integral.(9t 2/3 + 4t 7...
 5.23: In Exercises 1730, calculate the indefinite integral.sec2 x dx
 5.24: In Exercises 1730, calculate the indefinite integral.tan 3 sec 3 d
 5.25: In Exercises 1730, calculate the indefinite integral.(y + 2) 4 dy
 5.26: In Exercises 1730, calculate the indefinite integral.3x3 9 x2 dx
 5.27: In Exercises 1730, calculate the indefinite integral.(ex x) dx
 5.28: In Exercises 1730, calculate the indefinite integral.e4x dx
 5.29: In Exercises 1730, calculate the indefinite integral.4x1 dx
 5.30: In Exercises 1730, calculate the indefinite integral.sin(4x 9)dx
 5.31: In Exercises 3136, solve the differential equation with the given i...
 5.32: In Exercises 3136, solve the differential equation with the given i...
 5.33: In Exercises 3136, solve the differential equation with the given i...
 5.34: In Exercises 3136, solve the differential equation with the given i...
 5.35: In Exercises 3136, solve the differential equation with the given i...
 5.36: In Exercises 3136, solve the differential equation with the given i...
 5.37: Find f (t) if f (t) = 1 2t, f (0) = 2, and f (0) = 1.
 5.38: At time t = 0, a driver begins decelerating at a constant rate of 1...
 5.39: In Exercises 3942, use the given substitution to evaluate the integ...
 5.40: In Exercises 3942, use the given substitution to evaluate the integ...
 5.41: In Exercises 3942, use the given substitution to evaluate the integ...
 5.42: In Exercises 3942, use the given substitution to evaluate the integ...
 5.43: In Exercises 4392, evaluate the integral. 43. (20x4 9x3 2x) dx
 5.44: In Exercises 4392, evaluate the integral.2 0 (12x3 3x2)dx
 5.45: In Exercises 4392, evaluate the integral.(2x2 3x)2 dx
 5.46: In Exercises 4392, evaluate the integral.1 0 (x7/3 2x1/4)dx
 5.47: In Exercises 4392, evaluate the integral.x5 + 3x4 x2 dx
 5.48: In Exercises 4392, evaluate the integral.3 1 r4 dr
 5.49: In Exercises 4392, evaluate the integral.3 3 x2 4 dx
 5.50: In Exercises 4392, evaluate the integral.4 2 (x 1)(x 3) dx
 5.51: In Exercises 4392, evaluate the integral.3 1 [t] dt
 5.52: In Exercises 4392, evaluate the integral.2 0 (t [t]) 2 dt
 5.53: In Exercises 4392, evaluate the integral.(10t 7) 14 dt
 5.54: In Exercises 4392, evaluate the integral.3 2 7y 5 dy
 5.55: In Exercises 4392, evaluate the integral.(2x3 + 3x) dx (3x4 + 9x2)5
 5.56: In Exercises 4392, evaluate the integral.1 3 x dx (x2 + 5)2
 5.57: In Exercises 4392, evaluate the integral.. 5 0 15x x + 4 dx
 5.58: In Exercises 4392, evaluate the integral.t 2 t + 8 dt
 5.59: In Exercises 4392, evaluate the integral.1 0 cos 3 (t + 2) dt
 5.60: In Exercises 4392, evaluate the integral. /2 sin 5 6 d
 5.61: In Exercises 4392, evaluate the integral.t 2 sec2(9t 3 + 1)dt
 5.62: In Exercises 4392, evaluate the integral.sin2(3 ) cos(3)d
 5.63: In Exercises 4392, evaluate the integral.. csc2(9 2)d
 5.64: In Exercises 4392, evaluate the integral.sin 4 cos d
 5.65: In Exercises 4392, evaluate the integral./3 0 sin cos2/3 d
 5.66: In Exercises 4392, evaluate the integral.sec2 t dt (tan t 1)2
 5.67: In Exercises 4392, evaluate the integral.e92x dx
 5.68: In Exercises 4392, evaluate the integral.3 1 e4x3 dx
 5.69: In Exercises 4392, evaluate the integral.x2ex3 dx
 5.70: In Exercises 4392, evaluate the integral.ln 3 0 exex dx
 5.71: In Exercises 4392, evaluate the integral.ex 10x dx
 5.72: In Exercises 4392, evaluate the integral.e2x sin(e2x )dx
 5.73: In Exercises 4392, evaluate the integral.ex dx (ex + 2)3
 5.74: In Exercises 4392, evaluate the integral.sin cos ecos2 +1 d
 5.75: In Exercises 4392, evaluate the integral./6 0 tan 2 d
 5.76: In Exercises 4392, evaluate the integral.2/3 /3 cot 1 2 d
 5.77: In Exercises 4392, evaluate the integral.dt t (1 + (ln t)2)
 5.78: In Exercises 4392, evaluate the integral.cos(ln x) dx x
 5.79: In Exercises 4392, evaluate the integral.e 1 ln x dx x
 5.80: In Exercises 4392, evaluate the integral.dx x ln x
 5.81: In Exercises 4392, evaluate the integral.dx 4x2 + 9
 5.82: In Exercises 4392, evaluate the integral.0.8 0 dx 1 x2
 5.83: In Exercises 4392, evaluate the integral.12 4 dx x x2 1
 5.84: In Exercises 4392, evaluate the integral.3 0 x dx x2 + 9
 5.85: In Exercises 4392, evaluate the integral.3 0 dx x2 + 9
 5.86: In Exercises 4392, evaluate the integral.dx e2x 1
 5.87: In Exercises 4392, evaluate the integral.x dx 1 x4
 5.88: In Exercises 4392, evaluate the integral.5/ 2 5/ 2 dx 25 x2
 5.89: In Exercises 4392, evaluate the integral.4 0 dx 2x2 + 1
 5.90: In Exercises 4392, evaluate the integral.8 5 dx x x2 16
 5.91: In Exercises 4392, evaluate the integral.1 0 (tan1 x)3 dx 1 + x2
 5.92: In Exercises 4392, evaluate the integral.cos1 t dt 1 t2
 5.93: Combine to write as a single integral: 8 0 f (x) dx + 0 2 f (x) dx ...
 5.94: Let A(x) = x 0 f (x) dx, where f is the function shown in Figure 4....
 5.95: Find the local minima, the local maxima, and the inflection points ...
 5.96: Aparticle starts at the origin at time t = 0 and moves with velocit...
 5.97: On a typical day, a city consumes water at the rate of r(t) = 100 +...
 5.98: The learning curve in a certain bicycle factory isL(x) = 12x1/5 (in...
 5.99: Cost engineers at NASA have the task of projecting the cost P of ma...
 5.100: An astronomer estimates that in a certain constellation, the number...
 5.101: Evaluate 8 8 x15 dx 3 + cos2 x , using the properties of odd functi...
 5.102: Evaluate 1 0 f (x) dx, assuming that f is an even continuous functi...
 5.103: Plot the graph of f (x) = sin mx sin nx on [0, ] for the pairs (m, ...
 5.104: Show that x f (x) dx = xF (x) G(x) where F (x) = f (x) and G (x) = ...
 5.105: Prove 2 2 1 2x dx 4 and 1 9 2 1 3x dx 1 3
 5.106: Plot the graph of f (x) = x2 sin x, and show that 0.2 2 1 f (x) dx ...
 5.107: Find upper and lower bounds for 1 0 f (x) dx, for y = f (x) in Figu...
 5.108: In Exercises 108113, find the derivative. 108. A (x), where A(x) = ...
 5.109: In Exercises 108113, find the derivativeA ( ), where A(x) = x 2 cos...
 5.110: In Exercises 108113, find the derivatived dy y 2 3x dx
 5.111: In Exercises 108113, find the derivativeG (x), where G(x) = sin x 2...
 5.112: In Exercises 108113, find the derivativeG (2), where G(x) = x3 0 t ...
 5.113: In Exercises 108113, find the derivativeH (1), where H (x) = 9 4x2 ...
 5.114: Explain with a graph: If f is increasing and concave up on [a, b], ...
 5.115: Explain with a graph: If f is linear on [a, b], then the b a f (x) ...
 5.116: In this exercise, we prove x x2 2 ln(1 + x) x (for x > 0) 1 (a) Sho...
 5.117: Let F (x) = x x2 1 2 x 1 t2 1 dt Prove that F (x) and y = cosh1 x d...
 5.118: Let f be a positive increasing continuous function on [a, b], where...
 5.119: How can we interpret the quantity I in Eq. (2) if a
 5.120: The isotope thorium234 has a halflife of 24.5 days. (a) What is t...
 5.121: The Oldest Snack Food? In Bat Cave, New Mexico, archaeologists foun...
 5.122: The C14toC12 ratio of a sample is proportional to the disintegrat...
 5.123: What is the interest rate if the PV of $50,000 to be delivered in 3...
 5.124: An equipment upgrade costing $1 million will save a company $320,00...
 5.125: Find the PV of an income stream paying out continuously at a rate o...
 5.126: Calculate the limit: (a) lim n 1 + 4 n n (b) lim n 1 + 1 n 4n (c) l...
Solutions for Chapter 5: THE INTEGRAL
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 5: THE INTEGRAL
Get Full SolutionsChapter 5: THE INTEGRAL includes 126 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Since 126 problems in chapter 5: THE INTEGRAL have been answered, more than 41858 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Boundary
The set of points on the “edge” of a region

Compound interest
Interest that becomes part of the investment

Conditional probability
The probability of an event A given that an event B has already occurred

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

kth term of a sequence
The kth expression in the sequence

Modulus
See Absolute value of a complex number.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Positive angle
Angle generated by a counterclockwise rotation.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Rational zeros
Zeros of a function that are rational numbers.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

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

Solve by elimination or substitution
Methods for solving systems of linear equations.

Solve by substitution
Method for solving systems of linear equations.

System
A set of equations or inequalities.

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Vertical translation
A shift of a graph up or down.