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Example 12 - Find area bounded by y = 3x + 2, x = -1, 1 - Area bounded by curve and horizontal or vertical line

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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise
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Example 12 Find the area of region bounded by the line 𝑦=3𝑥+2, the 𝑥−𝑎𝑥𝑖𝑠 and the ordinates 𝑥=−1 and 𝑥=1 First Plotting 𝑦=3𝑥+2 In graph Area Required = Area ACB + Area ADE Area ACB Area ACB = −1﷮ −2﷮ 3﷯﷮𝑦 𝑑𝑥﷯ 𝑦→ equation of line Area ACB = −1﷮ −2﷮ 3﷯﷮ 3𝑥+2﷯ 𝑑𝑥﷯ Since Area ACB is below x-axis, it will come negative , Hence, we take modulus Area ACB = −1﷮ −2﷮ 3﷯﷮ 3𝑥+2﷯ 𝑑𝑥﷯﷯ = 3 𝑥﷮2﷯﷮2﷯+2𝑥﷯﷮−1﷮ −2﷮3﷯﷯﷯ = 3﷮2﷯ −2﷮3﷯﷯﷮2﷯+2×− 2﷮3﷯﷯﷯ − 3﷮2﷯ −1﷯﷮2﷯+2(−1)﷯ = 3﷮2﷯× 4﷮9﷯− 4﷮3﷯﷯− 3﷮2﷯−2﷯﷯ = −2﷮3﷯− − 1﷮2﷯﷯﷯ = −2﷮3﷯+ 1﷮2﷯﷯ = −1﷮6﷯﷯ = 1﷮6﷯ Area ADE Area ADE = −2﷮3﷯﷮1﷮𝑦 𝑑𝑥﷯ y → equation of line = −2﷮3﷯﷮1﷮ 3𝑥+2﷯𝑑𝑥﷯ = 3 𝑥﷮2﷯﷮2﷯+2𝑥﷯﷮ −2﷮3﷯﷮1﷯ = 3 (1)﷮2﷯﷮2﷯+2×1﷯ − 3﷮2﷯ −2﷮3﷯﷯﷮2﷯+2× −2﷮3﷯﷯﷯ = 3﷮2﷯+2﷯ − 2﷮3﷯− 4﷮3﷯﷯ = 7﷮2﷯+ 2﷮3﷯ = 25﷮6﷯ Thus, Required Area = Area ACB + Area ADE = 1﷮6﷯ + 25﷮6﷯ = 26﷮6﷯ = 13﷮3﷯

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