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Question
Find the area bounded by the curve y = x2 and the line y = 4.
Solution
Equation of the curve y = x2 ...(1)
Equation of the line y = 4 ...(2)
Solving equation (1) and (2)
x2 = 4
⇒ x = ± 2
Required Area
A = `int_(-2)^2 y_1 "d"x - int_(-2)^2 y_2 "d"x`
= `int_(-2)^2 4"d"x - int_(-2)^2 x^"d"x`
= `[4x]_(-2)^2 - [x^3/3]_(-2)^2`
= `[4(2) - 4(-2)] - [(2)^3/3 - (-2)^3/3]`
= `(8 + 8) - (8/3 + 8/3)`
= `16 - 16/3`
= `16[1 - 1/3]`
= `16(2/3)`
= `32/3` sq.units
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