InterviewSolution
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InterviewSolution
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Find ∫ 2x^3 e^x^2 dx.(a) -e^x^2 (x^2+2)+C(b) e^x^2 (x^2-1)+C(c) 2e^x^2 (x^2+1)+C(d) e^x^2 (x-1)+CThis question was addressed to me in an interview for job.This interesting question is from Integration by Parts topic in division Integrals of Mathematics – Class 12 |
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Answer» RIGHT choice is (B) e^x^2 (x^2-1)+C The EXPLANATION: Let x^2=t Differentiating w.r.t x, we get 2x DX=dt ∴∫ 2x^2 e^x^2 dx=∫ te^t dt By using the formula, ∫ U.v dx=u∫ v dx-∫ u’ (∫ v dx) ,we get ∫ t e^t dt=t∫ e^t dt-∫ (t)’∫ e^t dt =te^t-∫ e^t dt =te^t-e^t=e^t (t-1) Replacing t with x^2, we get ∫ 2x^3 e^x^2 dx=e^x^2 (x^2-1)+C |
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