Some Properties Of Definite Integrals

Step 1: Let

Step 2: Use property of definite integrals.
Here, So, Since , and :

Step 3: Add .

Step 4: Substitute .
When \Rightarrow , when \Rightarrow . So,

Final Answer:

Step 1: Use property of definite integrals.
Now,

Step 2: Add the two results.

Step 3: Final value.

Final Answer:

Step 1: Use property of definite integrals.
Let Using property:

Step 2: Add the two results.

Step 3: Simplify.
So,

Step 4: Substitution.
Put , limits .

Step 5: Evaluate.
So,

Final Answer: