$\int\limits_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x \text { is equal to }$
Solution
<p>$I = \int\limits_0^{20\pi } {{{\left( {|\sin x| + |\cos x|} \right)}^2}\,dx}$</p>
<p>$= 20\int\limits_0^\pi {\left( {1 + |\sin 2x|} \right)\,dx}$</p>
<p>$= 40\int\limits_0^{{\pi \over 2}} {(1 + \sin 2x)\,dx}$</p>
<p>$= \left. {40\left( {x - {{\cos 2x} \over 2}} \right)} \right|_0^{{\pi \over 2}}$</p>
<p>$= 40\left( {{\pi \over 2} + {1 \over 2} + {1 \over 2}} \right) = 20(\pi + 2)$</p>
About this question
Subject: Mathematics · Chapter: Definite Integration · Topic: Properties of Definite Integrals
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