Area bounded by the curve y= and the x-axis between x=0 and x=2 i… - Vidyadip

MCQ

Area bounded by the curve $\text{y}=\sin\text{x}$ and the $x-$axis between $\text{x}=0$ and $\text{x}=2\pi$ is:

A
$2\ sq$ units
B
$0\ sq$ units
C
$3\ sq$ units
✓
$4\ sq$ units

✓

Answer

Correct option: D.

$4\ sq$ units

$(d),$ as $\text{x}=\sin$ is positive in $1^{st}$ and $2^{nd}$ quadrant and negative is $3^{rd}$ and $4^{th}$ quadrant.
$=$Area$=\int\limits^{2\pi}_0\sin\text{x}\text{ dx}$
$=\int\limits^\pi_0\sin\text{x}+\int\limits^{2\pi}_\pi(-\sin\text{x})\text{dx}$
$=4\text{ sq}$ units

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