Question
Download Solution PDFComprehension
Direction : Consider the following for the items that follow :
Let
What is I equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Property of Definite Integrals (Symmetry):
- If
is continuous on , then . - This property helps in evaluating integrals involving trigonometric identities when limits are symmetric.
- Standard result used:
. - Combining two symmetrical integrals can simplify expressions and eliminate complex terms.
Calculation:
Let
⇒ Using substitution
⇒
⇒ Adding both expressions, we get:
⇒
⇒
⇒
⇒
∴ The value of the integral is
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