Some Properties Of Definite Integrals

Step 1: Concept
Use the property .
Step 2: Analysis
Let . Then . Adding the two equations: .
Step 3: Conclusion
.
Final Answer: (B)

Step 1: Relating the two integrals.
We are given two integrals and . Let us first examine : We can split the limits of the integral and compute the value of .

Step 2: Rewriting the integrals.
represents the integration of a function of , so from previous results we have:

Step 3: Conclusion.
Thus, is equal to , which matches option (C).

Concept: Use property:

Step 1: Let .

Step 2: Replace .


Step 3: Add both expressions.


Step 4: Solve.
Conclusion:
Answer =