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Ex 7.11, 21 - Value of log (4 + 3 sin x / 4 + 3 cos x) dx - Definate Integration by properties - P4

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Transcript

Ex 7.11, 21 Choose the correct answer : The value of 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 3 sin﷮𝑥﷯﷮4+3 cos﷮𝑥﷯﷯﷯𝑑𝑥﷯ is • 2 (B) 3﷮4﷯ (C) 0 (D) −2 Let I= 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 3 sin﷮𝑥﷯﷮4 + 3 𝑐𝑜𝑠 𝑥﷯﷯﷯𝑑𝑥 ∴ I = 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 3𝑠𝑖𝑛 𝜋﷮2﷯ − 𝑥﷯﷮4 + 3𝑐𝑜𝑠 𝜋﷮2﷯ − 𝑥﷯﷯﷯﷯𝑑𝑥 I = 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 𝑐𝑜𝑠𝑥﷮4 + 3 sin﷮𝑥﷯﷯﷯﷯𝑑𝑥 Adding (1) and (2) i.e. (1) + (2) I +I= 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 3 sin﷮𝑥﷯﷮4 + 3 cos﷮𝑥﷯﷯﷯﷯𝑑𝑥+ 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 3 cos﷮𝑥﷯﷮4 + 3 sin﷮𝑥﷯﷯﷯﷯𝑑𝑥 2I = 0﷮ 𝜋﷮2﷯﷮ 𝑙𝑜𝑔 4 + 3 sin﷮𝑥﷯﷮4 + 3 cos﷮𝑥﷯﷯﷯+𝑙𝑜𝑔 4 + 3 cos﷮𝑥﷯﷮4 + 3 sin﷮𝑥﷯﷯﷯﷯𝑑𝑥 ﷯ 2I = 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 4 + 3 sin﷮𝑥﷯﷮4 + 3 cos﷮𝑥﷯﷯﷯× 4 + 3 cos﷮𝑥﷯﷮4 + 3 sin﷮𝑥﷯﷯﷯𝑑𝑥 ﷯ 2I= 0﷮ 𝜋﷮2﷯﷮𝑙𝑜𝑔 1﷯𝑑𝑥﷯ 2I = 0 ∴ I = 0 ∴ Option C is correct.

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