InterviewSolution
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InterviewSolution
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The value of integral ` sum _(k=1)^(n) int _(0)^(1) f(k - 1+x) dx ` isA. ` int _(0)^(1) (x) dx`B. `int _(0)^(2) f(x) dx`C. ` int _(0)^(n) f(x) dx`D. ` n int _(0)^(1) f(x) dx` |
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Answer» Correct Answer - C Let `l=int_(0)^(1)f(k-1+x)dx` `rArr" "l=int_(k-1)^(k)f(t)dt," where "t=k-1+x` `rArr" "l=int_(k-1)^(k)f(x)dx` `therefore sum_(k=1)^(n)int_(k-1)^(k)f(x)dx=int_(0)^(1)f(x)dx+int_(1)^(2)f(x)dx+…+int_(n-1)^(n) f(x)dx=int_(0)^(n)f(x)dx` |
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