Page 1 Theorem If F is a particular antiderivative of f on an interval I, then every antiderivative of f on I is given by where c is an arbitrary constant, and all the antiderivatives of f on I can be obtained by assigning particular values for c. . () F x c Page 2 Theorem If F is a particular antiderivative of f on an interval I, then every antiderivative of f on I is given by where c is an arbitrary constant, and all the antiderivatives of f on I can be obtained by assigning particular values for c. . () F x c Notation 4 The symbol denotes the operation of antidifferentiation, and we write where F’( x)=f ( x), and c is an arbitrary constant. This is read “The indefinite integral of f(x) with respect to x is F(x) + c". ( ) ( ) f x dx F x c Page 3 Theorem If F is a particular antiderivative of f on an interval I, then every antiderivative of f on I is given by where c is an arbitrary constant, and all the antiderivatives of f on I can be obtained by assigning particular values for c. . () F x c Notation 4 The symbol denotes the operation of antidifferentiation, and we write where F’( x)=f ( x), and c is an arbitrary constant. This is read “The indefinite integral of f(x) with respect to x is F(x) + c". ( ) ( ) f x dx F x c In this notation, is the integral sign; f(x) is the integrand; dx is the differential of x which denotes the variable of integration; and c is called the constant of integration. 4 If the antiderivative of the function on interval I exists, we say that the function is integrable over the interval I. ( ) ( ) f x dx F x c Page 4 Theorem If F is a particular antiderivative of f on an interval I, then every antiderivative of f on I is given by where c is an arbitrary constant, and all the antiderivatives of f on I can be obtained by assigning particular values for c. . () F x c Notation 4 The symbol denotes the operation of antidifferentiation, and we write where F’( x)=f ( x), and c is an arbitrary constant. This is read “The indefinite integral of f(x) with respect to x is F(x) + c". ( ) ( ) f x dx F x c In this notation, is the integral sign; f(x) is the integrand; dx is the differential of x which denotes the variable of integration; and c is called the constant of integration. 4 If the antiderivative of the function on interval I exists, we say that the function is integrable over the interval I. ( ) ( ) f x dx F x c Integration Rules 1. Constant Rule. If k is any real number, then the indefinite integral of k with respect to x is 2. Coefficient Rule. Given any real number coefficient a and integrable function f, kdx kx C ( ) ( ) af x dx a f x dx Page 5 Theorem If F is a particular antiderivative of f on an interval I, then every antiderivative of f on I is given by where c is an arbitrary constant, and all the antiderivatives of f on I can be obtained by assigning particular values for c. . () F x c Notation 4 The symbol denotes the operation of antidifferentiation, and we write where F’( x)=f ( x), and c is an arbitrary constant. This is read “The indefinite integral of f(x) with respect to x is F(x) + c". ( ) ( ) f x dx F x c In this notation, is the integral sign; f(x) is the integrand; dx is the differential of x which denotes the variable of integration; and c is called the constant of integration. 4 If the antiderivative of the function on interval I exists, we say that the function is integrable over the interval I. ( ) ( ) f x dx F x c Integration Rules 1. Constant Rule. If k is any real number, then the indefinite integral of k with respect to x is 2. Coefficient Rule. Given any real number coefficient a and integrable function f, kdx kx C ( ) ( ) af x dx a f x dx Integration Rules 3. Sum and Difference Rule. For integrable functions f and g, 4. Power Rule. For any real number n, where n ? -1, the indefinite integral x n of is, 1 2 1 2 [ ( ) ( )] ( ) ( ) f x f x dx f x dx f x dx 1 1 n n x x dx C nRead More

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