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Definite Integration question

2003 · Shift 0 · Q115

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PYQ Library
JEE Main
Mathematics
Definite Integration
2003 · Shift 0 · Q115

Definite Integration question

2003 · Shift 0 · Q115

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

f\left( y \right) = {e^y},g\left( y \right) = y;y \gt 0

and

F\left( t \right) = \int\limits_0^t {f\left( {t - y} \right)g\left( y \right)dy,}

then :

A
$F\left( t \right) = t{e^{ - t}}$
B
$F\left( t \right) = 1t - t{e^{ - 1}}\left( {1 + t} \right)$
C
$F\left( t \right) = {e^t} - \left( {1 + t} \right)$
D
$F\left( t \right) = t{e^t}$ .

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