Question

The area of the region in the first quadrant enclosed by the graph of y = x(1 – x) and the x axis is A. 2/3 B. 1/3 C. 5/6 D. 1/6

Answer 1

D. 1/6

Explanation:

You want the area enclosed by the graph of y = x(1 -x) and the x-axis.

Integral

The area is the integral of the function value over the interval in which it is non-negative.

The zeros are at x=0 and x=1, so those are the limits of integration.

`\displaystyle \int_0^1{(x-x^2)}\,dx=\left[(x^2)/(2)-(x^3)/(3)\right]_0^1=(1)/(2)-(1)/(3)=(1)/(6)`

The enclosed area is 1/6 square units.

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