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The maximum value of \(\int\limits_{a-1}^{a+1}e^{-(x-1)^2}dx\) is attained (a is real ) at |
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Answer» the answer of the above qiestion is in the picture Let f(x) = \(\int\limits_{a-1}^{a+1}e^{-(x-1)^2}dx\) ∴ f'(x) = 0 gives -2(x - 1) \(e^{-(x-1)^2}\) = 0 ⇒ x - 1 = 0 (∵ e-(x - 1)2 \(\neq0\)) ⇒ x = 1 Now, f"(x) = \(e^{-(x-1)^2}\)(-2 + 4(x - 1)2) f"(1) = e0(-2 + 0) = -2 < 0 ∴ x = 1 is point of maxima Hence, maximum value of \(\int\limits_{a-1}^{a+1}e^{-(x-1)^2}dx \) is attained at x = 1 |
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