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Question

By using properties of definite integrals, evaluate the integrals
a0xx+axdx.

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Solution

Let Ia0xx+axdx.I=a0axax+a(ax)dx[a0f(x)dx=a0f(ax)dx]=a0axax+xdx
On adding Eqs. (i) and (ii), we get
2I=a0x+axax+xdx,2I=a01dx=[x]a0=a0=aI=a2


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