QuestionWrite the following expression as a single definite integral of the form .
Studdy Solution
STEP 1
1. We are given multiple definite integrals involving the same function .
2. The task is to combine these integrals into a single definite integral.
3. The properties of definite integrals, such as additivity and linearity, can be used to simplify the expression.
STEP 2
1. Use the additivity property of definite integrals to combine the integrals.
2. Simplify the resulting expression to a single definite integral.
STEP 3
Apply the additivity property of definite integrals. This property states that if , then:
Use this property to combine the first two integrals:
STEP 4
Subtract the third integral from the combined integral:
Use the property of definite integrals that states:
Apply this to simplify the expression:
The single definite integral is:
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