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