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Find the value of a such that the area bound between the curves $e^{(ax^2)}$ and $e^{1/8}$ and the lines x = 0 and x= 1 is minimum

I found out the point of intersection $\frac{1}{2 \sqrt{2a}}$ then found out the area after that used Newton lebnitz theorem and differentiated the function with respect to $a$. The issue I'm facing is that the final term I have to solve to obtain the value of a is of the form $$x^2 e^{x^2}$$

PradyumanDixit
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Avyansh Katiyar
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  • How did you obtain $a$ of that form? – Iceberry Oct 20 '18 at 12:04
  • What about area, question seems to lack something. – PradyumanDixit Oct 20 '18 at 14:45
  • @PradyumanDixit fixed it – Avyansh Katiyar Oct 20 '18 at 14:57
  • The area you are integrating over is not bound by the line $x=0$. In fact those curves and lines bound two distinct areas. I would say the question is ambiguous; are you meant to take the sum of the two areas? It's no good integrating $e^{ax^2}-e^{1/8}$ from $0$ to $1$, because that gives you the difference of the areas. So you have to be careful. – TonyK Oct 20 '18 at 15:08

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