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Question
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
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Solution
Let A be the required area
Given equation of the curve y = – 4x
∴ A = A1 + |A2|
= `int_(-1)^0 (-4x) "d"x + |int_0^2 (-4x) "d"x|`
= `-4[x^2/2]_0^1 + |-4[x^2/2]_0^2|`
= `2[0^2 - (-1)^2] + |-2(2^2 - 0^2)|`
= – 2(–1) + |– 2(4)|
= 2 + |– 8|
= 2 + 8
= 10 sq.units
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