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Find the area enclosed between y = cos x and X-axis between the lines x = π2 and x ≤ 3π2 - Mathematics and Statistics

Sum

Find the area enclosed between y = cos x and X-axis between the lines x = `pi/2` and x ≤ `(3pi)/2`

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Solution

Let A be the required area.

Consider the equation y = cos x.

∴ A = `int_(pi/2)^((3pi)/2) y  "d"x`

= `int_(pi/2)^((3pi)/2) cos x  "d"x`

= `[sin x]_(pi/2)^((3pi)/2)`

= `sin  (3pi)/2 - sin  pi/2`

= –1 – 1

= – 2

But, area cannot be negative.

∴ A = 2 sq.units

Concept: Area Between Two Curves
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