Question

The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is _____________ .

Options

• 2 sq. units

• 4 sq. units

• 3 sq. units

• 1 sq. unit

Answer 1

2 sq. units

 

The required area ABC,
\[A = \int_0^\pi y d x\]
\[ = \int_0^\pi \sin\left( x \right) d x\]
\[ = \left[ - \cos\left( x \right) \right]_0^\pi \]
\[ = - \cos\left( \pi \right) + \cos\left( 0 \right)\]
\[ = 1 + 1\]
\[ = 2\text{ square units }\]