Business I / Multiple Integration
Practice question · Estimate

Estimate ∫04(8−2x) dx\int_0^4 (8 - 2x)\, dx, the area of the triangle with base 4 and height 8.

Estimate on a scale from 0 to 40.

Hints
  1. The region under the line is a triangle.
  2. Half the base times the height gives the area.
Show the answer

16 (answers within ±2 count)

Why

∫04(8−2x) dx=[8x−x2]04=32−16=16\int_0^4 (8-2x)\, dx = [8x - x^2]_0^4 = 32 - 16 = 16. Or: triangle area =12×4×8=16= \frac{1}{2} \times 4 \times 8 = 16.

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