Attempt following question by selecting a choice to answer. f What is the area of the region bounded above by y = 2x^{2} and below by y = -2 over [-1, 1] ? ee ff A. f323 B. f163 C. f43 D. f83

Step 1: The region bounded above by y = 2x^{2} and below by y = - 2 over [-1, 1] is the shaded region in the fig.

Step 2: Since, the region R is the union of two regions R_{1} and R_{2} where R_{1} is the region bounded by y = 2x^{2}, x-axis over [-1,1] and R_{2} is the region bounded by y = -2, x-axis over [-1,1]

Step 3: The area of the shaded region = Area of R_{1} + Area of R_{2}[Figure.]

Step 4: = ∫-11 2x^{2}dx - ∫-11 (-2)dx[As y = 2x^{2} is above x-axis, y = - 2 is below x-axis.]

Step 5: = (23) [x^{3}]-11 + [2x]-11

Step 6: = (23) (2) + 2(2)

Step 7: = (43) + 4 = 163

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