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Example 29 - Chapter 7 Class 12 Integrals
Last updated at May 29, 2023 by Teachoo
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Example 29 You are here
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Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams
Chapter 7 Class 12 Integrals
Serial order wise
Transcript
Example 29 Evaluate −𝜋4𝜋4sin2𝑥 𝑑𝑥 Let f(x) = 𝑠𝑖𝑛2𝑥 f(-x) = 𝑠𝑖𝑛2−𝑥=−sin𝑥2=𝑠𝑖𝑛2𝑥 Since f(x) = f(-x) Hence, 𝑠𝑖𝑛2𝑥 is an even function −𝜋4𝜋4sin2𝑥 𝑑𝑥=0𝜋4sin2𝑥 𝑑𝑥 = 0𝜋41 − cos2 𝑥2 𝑑𝑥 = 20𝜋412−cos2𝑥2 𝑑𝑥 = 2 𝑥2−sin2𝑥2×20𝜋4 = 2 𝑥2−sin2𝑥40𝜋4 Putting Limits = 2𝜋412−sin2𝜋44 – 2 02−sin204 = 2𝜋8−sin𝜋24−0 = 2 𝜋8−14 = 𝝅𝟒−𝟏𝟐
