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Question

The numbers P, Q and R for which the function
f(x)=Pe2x+Qex+Rx satisfies the conditions
f(0)=1, f(log 2)=31 and log 40[f(x)Rx]dx=392 are
given by


A


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B


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C


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D


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Solution

The correct option is D



We have f(x)=2Pe2x+Qex+R
f(log 2)=8P+2Q+R
Also, 1=f(0)=P+Q
392=log 40[f(x)Rx]dx=log 40(Pe2x+Qex)dx
15P2+3Q=392
Now on solving the above equations, we get
P = 5, Q = -6 and R = 3


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