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Question

If 'a' is constant, then the value of the integral a20xeaxdx is _______
  1. 1

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Solution

The correct option is A 1
From integration by parts rule,
u dv = uv v du
Let u = x and dv=eaxdx. Then, du = dx and v=eaxa. Therefore

xeaxdx=x(eaxa)(eaxa)dx

=xeaxa1a2eax

Hence, 0xeaxdx=[xeaxa]0[1a2eax]0

=(00)1a2(01)=1a2

a20xeaxdx=a21a2=1

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