 5.2.1: A function F is an antiderivative of a function f on an intervalif ...
 5.2.2: Write an equivalent integration formula for each givenderivative fo...
 5.2.3: Evaluate the integrals.(a) [x3 + x + 5] dx (b) [sec2 x csc x cot x] dx
 5.2.4: The graph of y = x2 + x is an integral curve for the function f(x) ...
 5.2.5: A slope field for the differential equationdydx = 2xx2 4has a line ...
 5.2.6: 58 Find the derivative and state a corresponding integration formul...
 5.2.7: 58 Find the derivative and state a corresponding integration formul...
 5.2.8: 58 Find the derivative and state a corresponding integration formul...
 5.2.9: 910 Evaluate the integral by rewriting the integrand appropriately,...
 5.2.10: 910 Evaluate the integral by rewriting the integrand appropriately,...
 5.2.11: 1114 Evaluate each integral by applying Theorem 5.2.3 andFormula 2 ...
 5.2.12: 1114 Evaluate each integral by applying Theorem 5.2.3 andFormula 2 ...
 5.2.13: 1114 Evaluate each integral by applying Theorem 5.2.3 andFormula 2 ...
 5.2.14: 1114 Evaluate each integral by applying Theorem 5.2.3 andFormula 2 ...
 5.2.15: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.16: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.17: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.18: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.19: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.20: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.21: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.22: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.23: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.24: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.25: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.26: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.27: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.28: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.29: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.30: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.31: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.32: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.33: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.34: 1534 Evaluate the integral and check your answer by differentiating...
 5.2.35: Evaluate the integral 11 + sin x dxby multiplying the numerator and...
 5.2.36: Use the doubleangle formula cos 2x = 2 cos2 x 1 toevaluate the int...
 5.2.37: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.2.38: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.2.39: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.2.40: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.2.41: Use a graphing utility to generate some representative integralcurv...
 5.2.42: Use a graphing utility to generate some representative integralcurv...
 5.2.43: 4346 Solve the initialvalue problems. (a) dydx = 3 x, y(1) = 2(b) ...
 5.2.44: 4346 Solve the initialvalue problems. (a) dydx = 1(2x)3 , y(1) = 0...
 5.2.45: 4346 Solve the initialvalue problems. (a) dydx = 4ex , y(0) = 1 (b...
 5.2.46: 4346 Solve the initialvalue problems. (a) dydt = 31 t 2, y32= 0(b)...
 5.2.47: 4750 A particle moves along an saxis with position functions = s(t...
 5.2.48: 4750 A particle moves along an saxis with position functions = s(t...
 5.2.49: 4750 A particle moves along an saxis with position functions = s(t...
 5.2.50: 4750 A particle moves along an saxis with position functions = s(t...
 5.2.51: Find the general form of a function whose second derivativeis x. [H...
 5.2.52: Find a function f such that f (x) = x + cos x and suchthat f(0) = 1...
 5.2.53: 5357 Find an equation of the curve that satisfies the givenconditio...
 5.2.54: 5357 Find an equation of the curve that satisfies the givenconditio...
 5.2.55: 5357 Find an equation of the curve that satisfies the givenconditio...
 5.2.56: 5357 Find an equation of the curve that satisfies the givenconditio...
 5.2.57: 5357 Find an equation of the curve that satisfies the givenconditio...
 5.2.58: In each part, use a CAS to solve the initialvalue problem.(a) dydx...
 5.2.59: (a) Use a graphing utility to generate a slope field for the differ...
 5.2.60: (a) Use a graphing utility to generate a slope field forthe differe...
 5.2.61: 6164 The given slope field figure corresponds to one of thedifferen...
 5.2.62: 6164 The given slope field figure corresponds to one of thedifferen...
 5.2.63: 6164 The given slope field figure corresponds to one of thedifferen...
 5.2.64: 6164 The given slope field figure corresponds to one of thedifferen...
 5.2.65: Critique the following proof that an arbitrary constantmust be zero...
 5.2.66: Critique the following proof that an arbitrary constantmust be zero...
 5.2.67: (a) Show thatF (x) = tan1 x and G(x) = tan1(1/x)differ by a constan...
 5.2.68: Let F and G be the functions defined byF (x) = x2 + 3xx and G(x) =x...
 5.2.69: 6970 Use a trigonometric identity to evaluate the integral. tan2 x dx
 5.2.70: 6970 Use a trigonometric identity to evaluate the integral. cot2 x dx
 5.2.71: Use the identities cos 2 = 1 2 sin2 = 2 cos2 1 tohelp evaluate the ...
 5.2.72: Recall thatddx [sec1 x] =1xx2 1Use this to verify Formula 14 in T...
 5.2.73: The speed of sound in air at 0C (or 273 K on the Kelvinscale) is 10...
 5.2.74: Suppose that a uniform metal rod 50 cm long is insulatedlaterally, ...
 5.2.75: Writing What is an initialvalue problem? Describe thesequence of s...
 5.2.76: Writing What is a slope field? How are slope fields andintegral cur...
Solutions for Chapter 5.2: THE INDEFINITE INTEGRAL
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 5.2: THE INDEFINITE INTEGRAL
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Since 76 problems in chapter 5.2: THE INDEFINITE INTEGRAL have been answered, more than 39919 students have viewed full stepbystep solutions from this chapter. Chapter 5.2: THE INDEFINITE INTEGRAL includes 76 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Cotangent
The function y = cot x

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

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

Inverse cotangent function
The function y = cot1 x

Inverse variation
See Power function.

Leaf
The final digit of a number in a stemplot.

Logarithmic regression
See Natural logarithmic regression

Modulus
See Absolute value of a complex number.

Natural logarithm
A logarithm with base e.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Second quartile
See Quartile.

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

Variance
The square of the standard deviation.

Ymax
The yvalue of the top of the viewing window.