 6.1: The graph of a derivative f(x) is shown in Figure 6.32.Fill in the ...
 6.2: Figure 6.33 shows f. If F = f and F(0) = 0, find F(b)for b = 1, 2, ...
 6.3: In Exercises 34, graph F(x) such that F(x) = f(x) andF(0) = 0.3
 6.4: In Exercises 34, graph F(x) such that F(x) = f(x) andF(0) = 0.4
 6.5: (a) Using Figure 6.34, estimate  70 f(x)dx.(b) If F is an antideri...
 6.6: In Exercises 627, find the indefinite integrals.,5x dx
 6.7: In Exercises 627, find the indefinite integrals.,x3 dx
 6.8: In Exercises 627, find the indefinite integrals.,sin d
 6.9: In Exercises 627, find the indefinite integrals.,(x3 2) dx
 6.10: In Exercises 627, find the indefinite integrals., t2 +1t2dt
 6.11: In Exercises 627, find the indefinite integrals., 4t2 dt
 6.12: In Exercises 627, find the indefinite integrals.,(x2 + 5x + 8) dx
 6.13: In Exercises 627, find the indefinite integrals.,4w dw
 6.14: In Exercises 627, find the indefinite integrals.,(4t + 7) dt
 6.15: In Exercises 627, find the indefinite integrals.,cos d
 6.16: In Exercises 627, find the indefinite integrals.,tt +1ttdt 1
 6.17: In Exercises 627, find the indefinite integrals.,x +1xdx1
 6.18: In Exercises 627, find the indefinite integrals.,( + x11) dx
 6.19: In Exercises 627, find the indefinite integrals., 3 cos t + 3tdt
 6.20: In Exercises 627, find the indefinite integrals., y2 1y2dy 21
 6.21: In Exercises 627, find the indefinite integrals., 1cos2 x dx
 6.22: In Exercises 627, find the indefinite integrals., 2x + sin xdx 23
 6.23: In Exercises 627, find the indefinite integrals., x2 + x + 1xdx2
 6.24: In Exercises 627, find the indefinite integrals.,5ez dz
 6.25: In Exercises 627, find the indefinite integrals.,2x dx
 6.26: In Exercises 627, find the indefinite integrals.,(3 cos x7 sin x) dx
 6.27: In Exercises 627, find the indefinite integrals.,(2ex 8 cos x) dx
 6.28: In Exercises 2829, evaluate the definite integral exactly [asin ln(...
 6.29: In Exercises 2829, evaluate the definite integral exactly [asin ln(...
 6.30: For Exercises 3035, find an antiderivative F(x) withF(x) = f(x) and...
 6.31: For Exercises 3035, find an antiderivative F(x) withF(x) = f(x) and...
 6.32: For Exercises 3035, find an antiderivative F(x) withF(x) = f(x) and...
 6.33: For Exercises 3035, find an antiderivative F(x) withF(x) = f(x) and...
 6.34: For Exercises 3035, find an antiderivative F(x) withF(x) = f(x) and...
 6.35: For Exercises 3035, find an antiderivative F(x) withF(x) = f(x) and...
 6.36: Use the fact that (xx) = xx(1 + ln x) to evaluate exactly:, 31xx(1 ...
 6.37: Show that y = x + sin x satisfies the initial valueproblemdydx = 1 ...
 6.38: Show that y = xn + A is a solution of the differentialequation y = ...
 6.39: In Exercises 3942, find the general solution of the differential eq...
 6.40: In Exercises 3942, find the general solution of the differential eq...
 6.41: In Exercises 3942, find the general solution of the differential eq...
 6.42: In Exercises 3942, find the general solution of the differential eq...
 6.43: In Exercises 4346, find the solution of the initial value problem.d...
 6.44: In Exercises 4346, find the solution of the initial value problem.d...
 6.45: In Exercises 4346, find the solution of the initial value problem.d...
 6.46: In Exercises 4346, find the solution of the initial value problem.d...
 6.47: Find the derivatives in Exercises 4748.ddt , tcos(z3) dz
 6.48: Find the derivatives in Exercises 4748.ddx , 1xln t dt
 6.49: Use Figure 6.35 and the fact that F(2) = 3 to sketch thegraph of F(...
 6.50: The vertical velocity of a cork bobbing up and down onthe waves in ...
 6.51: In 5152, a graph of f is given. Let F(x) = f(x).(a) What are the x...
 6.52: In 5152, a graph of f is given. Let F(x) = f(x).(a) What are the x...
 6.53: The graph of f is given in Figure 6.37. Draw graphs off and f, assu...
 6.54: Assume f is given by the graph in Figure 6.38. Supposef is continuo...
 6.55: Use the Fundamental Theorem to find the area underf(x) = x2 between...
 6.56: Calculate the exact area between the xaxis and the graphof y = 7 8...
 6.57: Find the exact area below the curve y = x3(1 x) andabove the xaxis.
 6.58: Find the exact area enclosed by the curve y = x2(1x)2and the xaxis
 6.59: Find the exact area between the curves y = x2 andx = y2.
 6.60: Calculate the exact area above the graph of y = sin andbelow the gr...
 6.61: Find the exact area between f() = sin and g() =cos for 0 2.
 6.62: Find the exact value of the area between the graphs ofy = cos x and...
 6.63: Find the exact value of the area between the graphs ofy = sinh x, y...
 6.64: Use the Fundamental Theorem to determine the value ofb if the area ...
 6.65: Find the exact positive value of c if the area between thegraph of ...
 6.66: Use the Fundamental Theorem to find the average valueof f(x) = x2 +...
 6.67: The average value of the function v(x)=6/x2 on theinterval [1, c] i...
 6.68: In 6870, evaluate the expression using f(x) =5x., 41f1(x) dx
 6.69: In 6870, evaluate the expression using f(x) =5x., 41(f(x))1 dx
 6.70: In 6870, evaluate the expression using f(x) =5x., 41f(x) dx1
 6.71: In 7172, evaluate and simplify the expressionsgiven that f(t) = , t...
 6.72: In 7172, evaluate and simplify the expressionsgiven that f(t) = , t...
 6.73: Calculate the derivatives in 7376.ddx , x32sin(t2) dt
 6.74: Calculate the derivatives in 7376.ddx , 3cos xet2dt
 6.75: Calculate the derivatives in 7376.ddx , xxet4dt
 6.76: Calculate the derivatives in 7376.ddt , t3et1 + x2 dx
 6.77: A store has an inventory of Q units of a product at timet = 0. The ...
 6.78: For 0 t 10 seconds, a car moves along a straightline with velocityv...
 6.79: For a function f, you are given the graph of the derivativef in Fig...
 6.80: The acceleration, a, of a particle as a function of time isshown in...
 6.81: The angular speed of a car engine increases from 1100revs/min to 25...
 6.82: Figure 6.41 is a graph off(x) = x + 1, for 0 x 1;x 1, for 1 < x 2.(...
 6.83: If a car goes from 0 to 80 mph in six seconds with constantaccelera...
 6.84: A car going at 30 ft/sec decelerates at a constant 5 ft/sec2.(a) Dr...
 6.85: An object is thrown vertically upward with a velocity of80 ft/sec.(...
 6.86: If A(r) represents the area of a circle of radius r andC(r) represe...
 6.87: If V (r) represents the volume of a sphere of radius rand S(r) repr...
 6.88: A car, initially moving at 60 mph, has a constant decelerationand s...
 6.89: The birth rate, B, in births per hour, of a bacteria populationis g...
 6.90: Water flows at a constant rate into the left side of the Wshapedcon...
 6.91: In 9192, the quantity, N(t) in kg, of pollutant thathas leeched fro...
 6.92: In 9192, the quantity, N(t) in kg, of pollutant thathas leeched fro...
 6.93: Let f(x) have one zero, at x = 3, and suppose f(x) < 0for all x and...
 6.94: Let P(x) = , x0arctan(t2) dt.(a) Evaluate P(0) and determine if P i...
 6.95: (a) Set up a righthand Riemann sum for  ba x3dx usingn subdivisio...
 6.96: (a) Use a computer algebra system to find  e2x dx,  e3x dx, and ...
 6.97: (a) Use a computer algebra system to find  sin(3x) dx, sin(4x) dx...
 6.98: (a) Use a computer algebra system to find, x 2x 1 dx, , x 3x 1 dx, ...
 6.99: (a) Use a computer algebra system to find, 1(x 1)(x 3) dx, , 1(x 1)...
Solutions for Chapter 6: CONSTRUCTING ANTIDERIVATIVES
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 6: CONSTRUCTING ANTIDERIVATIVES
Get Full SolutionsSince 99 problems in chapter 6: CONSTRUCTING ANTIDERIVATIVES have been answered, more than 44956 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6: CONSTRUCTING ANTIDERIVATIVES includes 99 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612.

Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Arcsecant function
See Inverse secant function.

Chord of a conic
A line segment with endpoints on the conic

Composition of functions
(f ? g) (x) = f (g(x))

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Cycloid
The graph of the parametric equations

Data
Facts collected for statistical purposes (singular form is datum)

Directed distance
See Polar coordinates.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Parameter
See Parametric equations.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

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

Terms of a sequence
The range elements of a sequence.

Vertical asymptote
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a ƒ1x2 = q.