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`f(x)=min({x,x^(2)}` and `g(x)=max{x,x^(2)}`A. `int_(-1)^(1)f(x)=-(1)/(6)`B. `int_(-2)^(1)g(x)=(19)/(6)`C. `int_(-1)^(1)f(x)=(19)/(6)`D. `int_(-1)^(1)g(x)=-(1)/(6)` |
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Answer» Correct Answer - A::B `f(x)=min{x,x^(2)}` `g(x)=max(x,x^(2)}` `impliesf(x)={{:(x,xle0),(x^(2),00ltxne1),(x,-xgt1):}` and `{{:(x^(2),xle0),(x,0ltxne1),(x^(2),xgt1):}` (i). `int_(-1)^(1)f(x)=int_(-1)^(0)xdx+int_(0)^(1)xdx+int_(0)^(1)x^(2)dx` `=-(1)/(2)+(1)/(3)=-(1)/(6)` (ii). `int_(-2)^(1)g(x)=int_(-2)^(0)x^(2)dx+int_(0)^(1)xdx` `=(8)/(3)+(1)/(2)=(19)/(6)` |
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