A) \[-2\]
B) 3
C) 5
D) 8
E) \[-1\]
Correct Answer: C
Solution :
\[\int_{2}^{4}{[3-f(x)]}\,dx=7\] \[\Rightarrow \] \[[3x]_{2}^{4}-\int_{2}^{4}{f(x)}\,dx=7\] \[\Rightarrow \] \[6-\int_{2}^{4}{f(x)}\,dx=7\] \[\Rightarrow \] \[\int_{2}^{4}{f(x)}\,dx=-1\] ...(i) and \[\int_{-1}^{4}{f(x)}\,dx=4\] ...(ii) \[\int_{-1}^{4}{f(x)}\,dx=\int_{-1}^{2}{f(x)}\,dx+\int_{2}^{4}{f(x)}\,dx\] \[\Rightarrow \] \[4=\int_{-1}^{2}{f(x)}\,dx-1\] \[\Rightarrow \] \[=\int_{-1}^{2}{f(x)}\,dx=5\]You need to login to perform this action.
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