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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 March 23, 2023 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 ∫_(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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