f-x-2-x-1-7-x-1-0-4-f-x-dx-

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

f (x) = {_{2 x = 1}^{7 x \neq 1} \Rightarrow \int_{0}^{4} f (x) d x = ?

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

\int_{0}^{4} f (x) d x

= \int_{0}^{1} f (x) d x + \int_{1}^{4} f (x) d x

= \lim_{a \to 1^{-}} \int_{0}^{a} f (x) d x + \lim_{b \to 1^{+}} \int_{b}^{4} f (x) d x

= \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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