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Question
Find the area of the region bounded by the following curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
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Solution
Let A be the required area.
Consider the equation y = 2 – x2.
∴ A = `int_(-1)^(1) y*dx`
= `int_(-1)^(1)(2 - x^2)*dx`
= `[2x - x^3/3]_(-1)^(1)`
= `[2 xx 1 - 1^3/3] - [2 xx (-1) - (-1)^3/3]`
= `(2 - 1/3) - (-2 + 1/3)`
= `(5)/(3) - ((-5)/3)`
∴ A = `(10)/(3)` sq. units.
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