Evaluate the following integrals: ^2 _ 0 | |dx - Vidyadip

Question

Evaluate the following integrals:
$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}$

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Answer

$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}=\int^\limits{\pi}_{0}\sin\text{x }\text{dx}+\int^\limits{2\pi}_{\pi}-\sin\text{x }\text{dx}$
$=\big[-\cos\text{x}\big]^{\pi}_0+\big[\cos\text{x}\big]^{2\pi}_\pi$
$=\big[1+1\big]+\big[1+1\big]$
$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}=4$

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