Subscribe to our Youtube Channel - https://you.tube/teachoo

Last updated at Dec. 12, 2019 by Teachoo

Transcript

Ex 8.2, 4 Using integration find the area of region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2) Let points be A(– 1, 0), B(1, 3) and C(3, 2) We mark the points on the diagram Area Δ ABC = Area ABD + Area BDEC – Area ACE Area ABD Area ABD= ∫_(−1)^1▒〖𝑦 𝑑𝑥〗 𝑦→ Equation of line AB Equation of line between A(–1, 0) & B(1, 3) is (𝑦 − 0)/(𝑥 − (−1))=(3 − 0)/(1 − (−1)) 𝑦/(𝑥 + 1)=3/2 y = 3/2 (x + 1) Eq. of line b/w (x1, y1) & (x2, y2) is (𝑦 − 𝑦1)/(𝑥 − 𝑥1)=(𝑦2 − 𝑦1)/(𝑥2 − 𝑥1) Area ABD = ∫_(−1)^1▒〖𝑦 𝑑𝑥〗 = ∫1_(−1)^1▒〖3/2 (𝑥+1) 〗 dx = 3/2 ∫1_(−1)^1▒(𝑥+1) dx = 3/2 [𝑥^2/2+𝑥]_(−1)^1 = 3/2 [[1^2/2+1]−[(−1)^2/2+(−1)]] = 3/2 [[3/2]−[(−1)/2]] = 3/2 × 2 = 3 Area BDEC Area BDEC = ∫_1^3▒〖𝑦 𝑑𝑥〗 𝑦→ Equation of line BC (𝑦 − 3)/(𝑥 − 1)=(2 − 3)/(3 − 1) (𝑦 − 3)/(𝑥 − 1)=(−1)/2 2(y – 3) = –1(x – 1) 2y – 6 = –x + 1 2y = –x + 7 y = 1/2 (–x + 7) Eq. of line b/w (x1, y1) & (x2, y2) is (𝑦 − 𝑦1)/(𝑥 − 𝑥1)=(𝑦2 − 𝑦1)/(𝑥2 − 𝑥1) Area BDEC = ∫_1^3▒〖𝑦 𝑑𝑥〗 = ∫1_1^3▒〖1/2 (−𝑥+7)𝑑〗x = 1/2 [〖−𝑥〗^2/2+7𝑥]_1^3 = 1/2 [[〖−3〗^2/2+7(3)]− [〖(−1)/2〗^2+7(1)]] = 1/2 [(−9)/2+21+1/2−7] = 1/2 [(−9 + 1)/2+14] = 1/2 [(−8)/2+14] = 1/2 [−4+14] = 10/2 = 5 Area ACE Area ACE= ∫_(−1)^3▒〖𝑦 𝑑𝑥〗 𝑦→ Equation of line AC Equation of line between A(–1, 0) & C(3, 2) is (𝑦 − 0)/(𝑥 − (−1))=(2 − 0)/(3 − (−1)) 𝑦/(𝑥 + 1)=2/4 Eq. of line b/w (x1, y1) & (x2, y2) is (𝑦 − 𝑦1)/(𝑥 − 𝑥1)=(𝑦2 − 𝑦1)/(𝑥2 − 𝑥1) y = 1/2 (x + 1) Area ACE = ∫_(−1)^3▒〖𝑦 𝑑𝑥〗 = ∫1_(−1)^3▒〖1/2 (𝑥+1)𝑑〗x = 1/2 [𝑥^2/2+𝑥]_(−1)^3 = 1/2 [3^2/2+3−((−1)^2/2−1)] = 1/2 [9/2+3−(1/2−1)] = 1/2 [9/2+1/2+3+1] = 1/2 [4+4] = 4 Hence, Required area = Area ABD + Area BDEC − Area ACE = 3 + 5 − 4 = 4 square units

Ex 8.2

Ex 8.2,1
Not in Syllabus - CBSE Exams 2021

Ex 8.2, 2 Not in Syllabus - CBSE Exams 2021

Ex 8.2, 3 Important Not in Syllabus - CBSE Exams 2021

Ex 8.2, 4 Important Not in Syllabus - CBSE Exams 2021 You are here

Ex 8.2, 5 Important Not in Syllabus - CBSE Exams 2021

Ex 8.2, 6 Not in Syllabus - CBSE Exams 2021

Ex 8.2 , 7 Not in Syllabus - CBSE Exams 2021

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.