Misc 1 - Chapter 8 Class 12 Application of Integrals

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Misc 1 - Chapter 8 Class 12 Application of Integrals - Teachoo Find the area under the given curves and given lines: (i) 𝑦 = 𝑥2, 𝑥 = 1, 𝑥 = 2 and 𝑥-axis Area required = Area ABCD = ∫_1^2▒〖𝑦 𝑑𝑥〗 y → equation of parabola 𝑦=𝑥^2 =∫_1^2▒〖𝑥^2 𝑑𝑥〗 =[𝑥^3/3]_1^2 =1/3 [2^3−1^3 ] = 1/3 [8−1] =7/3 Misc 1 Find the area under the given curves and given lines: (ii) 𝑦= 𝑥4, 𝑥 = 1, 𝑥 = 5 and 𝑥-axis Area required = Area ABCD = ∫_1^5▒〖𝑦 𝑑𝑥〗 Here, 𝑦=𝑥^4 =∫_1^5▒〖𝑥^4 𝑑𝑥〗 =[𝑥^5/5]_1^5 =5^5/5−1^5/5 =5^4−1/5 = 625 – 0.2 = 624.8