jee-main 2022 Q75

jee-main · India · session1_27jun_shift2 Indefinite & Definite Integrals Piecewise/Periodic Function Integration

The integral $\int _ { 0 } ^ { 1 } \frac { 1 } { 7 ^ { \left[ \frac { 1 } { x } \right] } } d x$, where $[ \cdot ]$ denotes the greatest integer function, is equal to
(1) $1 - 6 \ln \left( \frac { 6 } { 7 } \right)$
(2) $1 + 6 \ln \left( \frac { 6 } { 7 } \right)$
(3) $1 - 7 \ln \left( \frac { 6 } { 7 } \right)$
(4) $1 + 7 \ln \left( \frac { 6 } { 7 } \right)$

The integral $\int _ { 0 } ^ { 1 } \frac { 1 } { 7 ^ { \left[ \frac { 1 } { x } \right] } } d x$, where $[ \cdot ]$ denotes the greatest integer function, is equal to\\
(1) $1 - 6 \ln \left( \frac { 6 } { 7 } \right)$\\
(2) $1 + 6 \ln \left( \frac { 6 } { 7 } \right)$\\
(3) $1 - 7 \ln \left( \frac { 6 } { 7 } \right)$\\
(4) $1 + 7 \ln \left( \frac { 6 } { 7 } \right)$

Paper Questions

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