If $f\,\,\left( x \right) = a{e^{2x}}\, + \,b{e^x}\,\, + \,\,c{\rm{ }}x$ satisfies the conditions $f\left( 0 \right) = - 1,\,\,f'\left( {\log \,\,2} \right) = 31,\,\,\mathop \smallint \limits_0^{\log 4} \,\,\left( {\,f\,\,\left( x \right)\,\, - \,\,c{\rm{ }}x} \right)\,\,dx = \frac{{39}}{2}$, then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f\,\,\left( x \right) = a{e^{2x}}\, + \,b{e^x}\,\, + \,\,c\mathrm{ }x

satisfies the conditions

f\left( 0 \right) = - 1,\,\,f'\left( {\log \,\,2} \right) = 31,\,\,\int \limits_0^{\log 4} \,\,\left( {\,f\,\,\left( x \right)\,\, - \,\,c\mathrm{ }x} \right)\,\,dx = \frac{{39}}{2}

, then

View answer and explanation

Correct option: A

a = 5,\,\,b = - 6,\,\,c = - \,7

Option A (

a = 5,\,\,b = - 6,\,\,c = - \,7

) is correct because it satisfies all three given conditions when substituted into the function and its derivative.