Question
Find the area bounded by the curve $\text{y}=\sin\text{x}$ between x = 0 and $\text{x}=2\pi.$
✓
Answer
Required area $=\int\limits^{2\pi}_0\sin\text{x dx}=\int\limits^{\pi}_0\sin\text{x dx}+\Big|\int\limits^{2\pi}_\pi\sin\text{x dx}|$ $=-\big[\cos\text{x}\big]^\pi_0+\Big|\big[-\cos\text{x}\big]^{2\pi}_\pi\Big|$ $=-\big[\cos\pi-\cos0\big]+\Big|-\big[\cos2\pi-\cos\pi\big]\Big|$
$=-\big[-1-1\big]+\big|-(1+1)\big|$ $=2+2=4\text{ sq. units}$
$=-\big[-1-1\big]+\big|-(1+1)\big|$ $=2+2=4\text{ sq. units}$
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