The area bounded by the curve $y = f (x)$ the co- ordinates axes & the line $x = x_{1}$ is given by $x_{1} . e^{x 1} .$ therefore f(x) equals :

e^{x}

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x e^{x}

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x e^{x} - e^{x}

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x e^{x} + e^{x}

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Solution

The correct option is D $x e^{x} + e^{x}$
Since, Area $= \int_{0}^{x_{1}} f (x) = x_{1} e^{x^{1}}$
we can say that,
$\Rightarrow \int_{0}^{x} f (x) = x e^{x}$
so, using newton-leibrite formula and differentiating, we get
$\Rightarrow f (x) = x e^{x} + e^{x} = e^{x} (x + 1)$
Hence, the answer is $e^{x} (x + 1) .$

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