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Ex 7.9, 9 - Direct integrate dx / root 1 - x2 - Ex 7.9

Ex 7.9, 9 - Chapter 7 Class 12 Integrals - Part 2

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Transcript

Ex7.9, 9 0﷮1﷮ 𝑑𝑥﷮ ﷮1−𝑥2﷯﷯﷯ Step 1 :- Let F 𝑥﷯= ﷮﷮ 𝑑𝑥﷮ ﷮1 − 𝑥﷮2﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮ 1﷮2﷯ − 𝑥﷮2﷯﷯﷯﷯ = sin﷮−1﷯﷮ 𝑥﷮1﷯﷯ =𝑠𝑖 𝑛﷮−1﷯ 𝑥 Hence F 𝑥﷯=𝑠𝑖 𝑛﷮−1﷯ 𝑥 Step 2 :- 0﷮1﷮ 𝑑𝑥﷮ ﷮1 − 𝑥﷮2﷯﷯﷯=𝐹 1﷯−𝐹 0﷯﷯ =𝑠𝑖 𝑛﷮−1﷯ 1﷯−𝑠𝑖 𝑛﷮−1﷯ 0﷯ = 𝜋﷮2﷯−0 = 𝜋﷮2﷯

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