Area between the curve y - cos x and x- axis when 0 - x is -MP PET 1997-

Y=cos x, When x ϵ [ 0,π/2 ], cos x ≥ 0 When x ϵ [ π/2,3π/2 ], cos x ≤ 0 When x ϵ [ 3π/2,2 π ], cos x ≥ 0 Thus required area is given by, ∫_0^π/2y dx=∫_0^π/2co ...

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Standard XIII

Mathematics

Property 7

Area between ...

Question

Area between the curve y = cos x and x- axis when 0 $\leq$ x is [MP PET 1997]

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Solution

The correct option is B
4

$y = c o s x, W h e n x ϵ [0, \frac{π}{2}], c o s x \geq 0$
$W h e n x ϵ [\frac{π}{2}, \frac{3 π}{2}], c o s x \leq 0$
$W h e n x ϵ [\frac{3 π}{2}, 2 π], c o s x \geq 0$
Thus required area is given by,
$\int_{0}^{\frac{π}{2}} y d x = \int_{0}^{\frac{π}{2}} c o s x d x + \int_{\frac{π}{2}}^{\frac{3 π}{2}} (- c o s x) d x + \int_{\frac{3 π}{2}}^{2 π} c o s x d x$
= 1 + 2 + 1 = 4sq.unit

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