𝑓(𝑥)={2𝑥−8 8−2𝑥 if 0≤𝑥<4, if 4≤𝑥≤8. Evaluate the definite integral by interpreting it in terms of signed area. ∫80𝑓(𝑥)𝑑𝑥=

Answer 1

Split the integral into regions of particular f(x) functions:

int from 0 to 8 of f(x)dx = int from 0 to 4 of (2x-8)dx + int from 4 to 8 of (8-2x)dx

Note that f(x) is continuous at 4.

x²-8x |₀⁴ + 8x - x²|₄⁸ = 16-32+64-64-(32-16) = -32

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