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∫ (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 ∫_(βˆ’π‘Ž)π‘Ž 𝑓(π‘₯)𝑑π‘₯=0,γ€— if f(βˆ’π‘₯)=βˆ’π‘“(π‘₯) And ∫_(βˆ’π‘Ž)^π‘Žπ‘“(π‘₯)𝑑π‘₯=2∫_0^π‘Žπ‘“(π‘₯)𝑑π‘₯ , if f(βˆ’π‘₯)=𝑓(π‘₯) Now, ∫_(βˆ’2)^2(π‘₯^3+1)𝑑π‘₯ = ∫_(βˆ’2)^2 π‘₯^3 𝑑π‘₯γ€— + ∫_(βˆ’2)^21𝑑π‘₯ Since γ€–(βˆ’π‘₯)γ€—^3=βˆ’π‘₯^3 So, ∫_(βˆ’π‘Ž)^π‘Žβ–’γ€–π‘₯^3 𝑑π‘₯=0,γ€— And 1 is constant, so f(–x) = f(x) ∫_(βˆ’π‘Ž)^π‘Žβ–’1𝑑π‘₯=2∫_0^π‘Žβ–’π‘‘π‘₯ = 0 + 2∫_0^2β–’1𝑑π‘₯ = 2∫_0^2▒𝑑π‘₯ = 2 γ€–[π‘₯]γ€—_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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.