Question
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Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Definite Integral:
If ∫ f(x) dx = g(x) + C, then
Properties:
- For even functions: f(-x) = f(x). And
. - For odd functions: f(-x) = -f(x). And
. . - If f(x) = f(2a - x), then
.
Calculation:
It can be observed that sin (-θ) = -sin θ.
Let f(x) = |sin x|
Put x = -x
⇒ f(-x) = |sin -x| = |-sin x| = |sin x| = f(x)
∴ |sin x| is an even function.
Therefore, using the properties of definite integrals, we get:
= 2
= 2
= -2
= -2[0 - 1]
= 2.
Last updated on May 30, 2025
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