definite1

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saikat007 mukherjee ·

puting x=0 in the equation, we have,
0= 1 - c.1.[lim 0 to 1∫f(t)e-t dt]
or, lim 0 to 1 ∫f(t)e-tdt=1c
now differentiating the equation,
f(x)= ex - 2e2x.c.1c
or, f(x)= ex - 2e2x
now, lim 0 to 1 ∫f(x)e-xdx= lim 0 to 1 ∫(1 - 2ex)dx = 3 - 2e
so c= 13-2e

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