Given-f-x-1-x-x-1-x-1-x-gt-1-find-3-8-f-x-1-f-x-1-dx-

Question Number 161229 by cortano last updated on 14/Dec/21

G i v e n f (x) = {\begin{cases} 1 - ∣ x ∣; x ⩽ 1 \\ ∣ x ∣ - 1; x > 1 \end{cases}

f i n d \int_{- 3}^{8} [f (x - 1) + f (x + 1)] d x .

Answered by mr W last updated on 14/Dec/21

Commented by mr W last updated on 14/Dec/21

r e d : f (x)

b l u e : f (x - 1)

g r e e n : f (x + 1)

\int_{- 3}^{8} f (x - 1) d x = - \frac{3 \times 3}{2} + \frac{2 \times 1}{2} + \frac{6 \times 6}{2} = \frac{29}{2}

\int_{- 3}^{8} f (x + 1) d x = - \frac{1 \times 1}{2} + \frac{2 \times 1}{2} + \frac{8 \times 8}{2} = \frac{65}{2}

\int_{- 3}^{8} [f (x - 1) + f (x + 1)] d x = \frac{29 + 65}{2} = 47

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