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Ex 7.11, 13 - Using properties of definite integrals sin7 x dx - Definate Integration by properties - P7

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Ex 7.11, 13 By using the properties of definite integrals, evaluate the integrals : − 𝜋﷮2﷯﷮ 𝜋﷮2﷯﷮ sin﷮7﷯﷮𝑥﷯﷯ 𝑑𝑥 This is of form −𝑎﷮𝑎﷮𝑓 𝑥﷯𝑑𝑥﷯ 𝑓 𝑥﷯= sin﷮7﷯﷮𝑥﷯ 𝑓 −𝑥﷯= sin﷮7﷯﷮ −𝑥﷯﷯= −𝑠𝑖𝑛𝑥﷯﷮7﷯= −1﷯﷮7﷯ 𝑠𝑖𝑛𝑥﷯﷮7﷯=− sin﷮7﷯﷮𝑥﷯ Thus, 𝑓 −𝑥﷯ =− 𝑓﷮ 𝑥﷯﷯ ∴ −𝜋﷮2﷯﷮ 𝜋﷮2﷯﷮ sin﷮7﷯﷮𝑥 𝑑𝑥=𝟎﷯﷯

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