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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 3 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 Now, 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 square units Area ADE Area ADE = ∫1_((−𝟐)/𝟑)^𝟏▒〖𝒚 𝒅𝒙〗 y → equation of line = ∫1_((−𝟐)/𝟑)^𝟏▒(𝟑𝒙+𝟐)𝒅𝒙 = [(3𝑥^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 square units Thus, Required Area = Area ACB + Area ADE = 1/6 + 25/6 = 26/6 = 𝟏𝟑/𝟑 square units

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.