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Question Number 203186 by lorance last updated on 11/Jan/24

$$f\left(x\right)=\{{}_{2x=1}^{7x\ne 1}\Rightarrow {\int }_0^{4}f\left(x\right)dx=?$$

Answered by mr W last updated on 12/Jan/24

$${\int }_0^{4}f\left(x\right)dx$$$$={\int }_0^{1}f\left(x\right)dx+{\int }_1^{4}f\left(x\right)dx$$$$=\underset{a\to 1^{-}}{\lim }{\int }_0^{a}f\left(x\right)dx+\underset{b\to 1^{+}}{\lim }{\int }_b^{4}f\left(x\right)dx$$$$=\underset{a\to 1^{-}}{\lim 7}\times (a-0)+\underset{b\to 1^{+}}{\lim 7}\times (4-b)$$$$=7\times (1-0)+7\times (4-1)$$$$=7\times (4-0)$$$$=28$$

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