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The value of\mathrm{ \int_{-1}^1 g(x)-g-(-x)+[x] d x } where [.] is the greatest function and \mathrm{g}(\mathrm{x}) continuous and differentiable for all x is

Option: 1

g^{\prime}(1)-g^{\prime}(-1)-2


Option: 2

g^{\prime}(1) g^{\prime}(1)+2


Option: 3

2


Option: 4

1


Answers (1)

best_answer

\mathrm{g(x)-g(x)} is odd function

\mathrm{ \begin{aligned} & \Rightarrow \quad \int_{-1}^{+1} g(x)-g(-x) d x=0 \\ & \text { Therefore } \int_{-1}^1[x] d x=1 \end{aligned} }

Posted by

himanshu.meshram

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