Ex 8.2, 5 - Find area of triangular region y = 2x + 1, y=3x+1 - Ex 8.2

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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise
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Ex 8.2 , 5 Using integration find the area of the triangular region whose sides have the equations 𝑦=2𝑥+1, 𝑦=3𝑥+1 and 𝑥=4 Step 1: Draw the figure & x = 4 Required Area = Area ABC Finding point of Intersection B & C For B B is intersection of y = 3x + 1 & x = 4 Putting x = 4 in y = 3x + 1 y = 3(4) + 1 = 13 So, B(4, 13) For C C is intersection of y = 2x + 1 & x = 4 Putting x = 4 in y = 2x + 1 y = 2(4) + 1 = 9 So, C(4, 9) Finding Area Required Area ABC = Area OABD – Area OACD Area OABD Area OABD = 0﷮4﷮𝑦 𝑑𝑥﷯ where y = 3x + 1 = 2 ×4﷮2﷯﷮2﷯+4− 2 × 0﷮2﷯﷮2﷯+0﷯﷯ = 16 + 4 − 0 = 20 Area Required = Area ABDO − Area ACDO = 28 − 20 = 8 unit2

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