Question

The area of the region bounded by the curve y = sin x between x = - π and x = `(3pi)/2` is ______.

विकल्प

• 1 (unit)²

• 3 (unit)²

• 5 (unit)²

• 2 (unit)²

Answer 1

The area of the region bounded by the curve y = sin x between x = - π and x = `(3pi)/2` is 5 (unit)².

Explanation:

Given curve, 

y = sin x

x = - π = `(3pi)/2`

Area of shaded region,

`|int_(- pi)^0 sin x  dx| + int_0^pi sin x  dx + |int_pi^(pi//2) sin x  dx|`

`|- [cos x]_(- pi)^0| + [- cos x]_0^pi + |- [cos x]_pi^((3pi)/2)|`

= |- 1 - 1| + (1 + 1) + |0 - 1|

= 2 + 2 + 1

= 5 sq unit