CBSE Class 12 Sample Paper for 2020 Boards

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 17 - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by

Evaluate

∫ (x 3 + 1) dx from -2 to 2

Evaluate integral (x^3 + 1) dx from -2 to 2 - Teachoo - CBSE Class 12

Question 17 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2
Question 17 - CBSE Class 12 Sample Paper for 2020 Boards - Part 3

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Question 17 ∫ (x3 + 1) dx from -2 to 2 This is of form ∫ a -a f (x) dx And we now that ∫_(−𝑎)𝑎 𝑓(𝑥)𝑑𝑥=0,〗 if f(−𝑥)=−𝑓(𝑥) And ∫_(−𝑎)^𝑎𝑓(𝑥)𝑑𝑥=2∫_0^𝑎𝑓(𝑥)𝑑𝑥 , if f(−𝑥)=𝑓(𝑥) Now, ∫_(−2)^2(𝑥^3+1)𝑑𝑥 = ∫_(−2)^2 𝑥^3 𝑑𝑥〗 + ∫_(−2)^21𝑑𝑥 Since 〖(−𝑥)〗^3=−𝑥^3 So, ∫_(−𝑎)^𝑎▒〖𝑥^3 𝑑𝑥=0,〗 And 1 is constant, so f(–x) = f(x) ∫_(−𝑎)^𝑎▒1𝑑𝑥=2∫_0^𝑎▒𝑑𝑥 = 0 + 2∫_0^2▒1𝑑𝑥 = 2∫_0^2▒𝑑𝑥 = 2 〖[𝑥]〗_0^2 = 2 (2 – 0) = 4

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo