Question

# If 'a' is constant, then the value of the integral a2∞∫0xe−axdx is _______1

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Solution

## The correct option is A 1From integration by parts rule, ∫u dv = uv−∫ v du Let u = x and dv=e−axdx. Then, du = dx and v=e−ax−a. Therefore ∫xe−axdx=x(e−ax−a)−∫(e−ax−a)dx =−xe−axa−1a2e−ax Hence, ∫∞0xe−axdx=[−xe−axa]∞0−[1a2e−ax]∞0 =(0−0)−1a2(0−1)=1a2 a2∞∫0xe−axdx=a2⋅1a2=1

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