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crystal271

28.09.2020

Mathematics

The area of interest is symmetrical about the origin, so can be found by doubling the integral for the area in the first quadrant. Then the total area is
$A= 2\int\limits^{0.5}_{0}{(1-2x^2-x)} \, dx =2\left(0.5-\frac{2}{3}0.5^{3}-\frac{1}{2}0.5^2\right)\\A=1-\frac{1}{6}-\frac{1}{4}=1-\frac{5}{12}\\\\A=\dfrac{7}{12}$
Find the area of the region bounded by the curves of y=1-2x^2 and y=|x|

Find the area of the region bounded by the curves of y=1-2x^2 and y=|x|

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