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प्रश्न
Find the area enclosed between the X-axis and the curve y = sin x for values of x between 0 to 2π
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उत्तर
Let A be the required area.
Consider the equation y = sin x.
A1 = `int_0^"a" sin x "d"x`
= `[- cos x]_0^pi`
= – (cos π – cos 0)
= – (–1 – 1)
= 2
A2 = `int_pi^(2pi)sinx "d"x`
= `[- cos x]_pi^(2pi)`
= –[1 – (– 1)]
= – 2
∴ A = A1 + |A2|
= 2 + |(– 2)|
= 4 sq.units
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