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Area of Bounded Regions · Question 4 of 115

Question 4

EasyOriginal question

Using integration, what is the area of the region bounded by the line x+2y=8x + 2y = 8 and the coordinate axes?

Options for question 4

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The line meets the axes at (8,0)(8, 0) and (0,4)(0, 4); above the xx-axis it is y=4−x2y = 4 - \frac{x}{2}.

  2. ∫08(4−x2)dx=32−16=16\int_0^{8} \left(4 - \frac{x}{2}\right)dx = 32 - 16 = 16 square units.

Worth noting

32 is the rectangle 8×48 \times 4, twice the triangle; 12 stops the integral at x=4x = 4, the yy-intercept.

Concept
Area of a region bounded by lines
Typical time
60 s
Your time
—
The rule this testsRegions with lines
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