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Mathematical Expression Editor
In this section we examine several properties of the indefinite integral.
Properties of Indefinite Integrals
Constant Multiple Rule where c is a constant.
1
Compute
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Compute
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Compute
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Compute
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Compute
Do not add the +C to your answer
Compute
Do not add the +C to your answer
Compute
Do not add the +C to your answer
Compute
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Compute
Do not add the +C to your answer
Compute
Do not add the +C to your answer
Compute
Use the power rule with
The Power Rule says C
Do not add the +C to your answer
Compute
Use the power rule with
The Power Rule says C
Do not add the +C to your answer
Compute
Negative exponents:
Use the power rule with
The Power Rule says C
Do not add the +C to your answer
Compute
Negative exponents:
Use the power rule with
The Power Rule says C
Do not add the +C to your answer
Compute
Rational exponents:
Use the power rule with
The Power Rule says C
Do not add the +C to your answer
Compute
Rational exponents:
Use the power rule with
The Power Rule says C
Do not add the +C to your answer
Sum And Difference Rules The integral of a sum or difference is the sum or difference
of the integrals:
Compute
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Compute
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Compute
Compute
Compute
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Compute
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Compute
Distribute
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Compute
Compute
Compute
Divide each term by
Use the power rule where appropriate ()
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Compute
Compute
Distribute the x (add exponents)
Use the power rule where appropriate ()
Do not add the +C to your answer
Compute
Initial Value Problems
One reason we might be interested in computing an indefinite integral is to solve a
differential equation. Consider the following initial value problem: Given, and , find . The condition, , is called an initial condition. The main step in slving this problem is
to observe that the function that we seek is an anti-derivative of the given function .
Hence, to find we will compute the definite integral,
Lets look at some examples.
Solve the initial value problem:
First, Then, we use the initial condition, , to find the appropriate value of the
constant . which yields . So, the final answer is
Solve the initial value problem:
First, Then, we use the initial condition, , to find the appropriate value of the
constant . which yields . So, the final answer is