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Question
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
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Solution
A = (Area below X-axis) + (Area above X-axis)
Required area A = A1 + |A2|
A = `int_-1^0 (-2x) dx + |int_0^2(-2x)dx|`
= `[-2 x^2/2]_-1^0 + [(2x^2)/2]_0^2`
= `[-x^2]_-1^0 + [x^2]_0^2`
= (0 + 1) + (4 − 0)
A = 5 sq. units
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