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What is the area of the figure enclosed by the curve y = 2x2, the straight line y = - 4x-2, and the straight line y = 1 The area of the figure enclosed by the curve y = 2x2, the straight line y = - 4x-2 and the straight line x = 1 is
Drawing shows that the enclosed figure is an approximate triangle figure composed of two straight lines and one curve
This is a problem of definite integral. Let's calculate the intersection first
Let the intersections be a, B and C
A (- 1,2) B (- radical 2 / 2,1) C (- 3 / 4,1) can be obtained by simultaneous equations
Then use the idea of segmentation, into several basic graphics, respectively integral
The segmentation method is not unique. The result is: 7 / 8 - (4-radical 2) / 3
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