Evaluate
β« (x ^{ 3 } + 1) dx from -2 to 2
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CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
Last updated at March 23, 2023 by Teachoo
Get live Maths 1-on-1 Classs - Class 6 to 12
Question 17 β« (x3 + 1) dx from -2 to 2 This is of form β« a -a f (x) dx And we now that β«_(βπ)π π(π₯)ππ₯=0,γ if f(βπ₯)=βπ(π₯) And β«_(βπ)^ππ(π₯)ππ₯=2β«_0^ππ(π₯)ππ₯ , if f(βπ₯)=π(π₯) Now, β«_(β2)^2(π₯^3+1)ππ₯ = β«_(β2)^2 π₯^3 ππ₯γ + β«_(β2)^21ππ₯ Since γ(βπ₯)γ^3=βπ₯^3 So, β«_(βπ)^πβγπ₯^3 ππ₯=0,γ And 1 is constant, so f(βx) = f(x) β«_(βπ)^πβ1ππ₯=2β«_0^πβππ₯ = 0 + 2β«_0^2β1ππ₯ = 2β«_0^2βππ₯ = 2 γ[π₯]γ_0^2 = 2 (2 β 0) = 4