Question

Can anyone please solve this? ​

Answer 1

$\maltese\:\underline{\underline{\textsf{Answer :}}}\maltese$

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$\longrightarrow \: \displaystyle \rm y = \int\limits_{- 4}^{ - 1} \dfrac{\pi}{2} \, d \theta$

$\longrightarrow \: \displaystyle \rm y = \dfrac{\pi}{2} \int\limits_{- 4}^{ - 1} \, d \theta$

$\longrightarrow \: \displaystyle \rm y = \dfrac{\pi}{2}\Bigg[ \theta\Bigg]_{ - 4}^{ - 1}$

$\longrightarrow \: \displaystyle \rm y = \dfrac{\pi}{2}\Bigg[ - 1 - ( - 4)\Bigg]$

$\longrightarrow \: \displaystyle \rm y = \dfrac{\pi}{2}\Bigg[ - 1 + 4\Bigg]$

$\longrightarrow \: \displaystyle \rm y = \dfrac{\pi}{2}\bigg[ 3\bigg]$

$\longrightarrow \: \displaystyle \underline{ \underline{\rm y = \dfrac{3\pi}{2}}}$

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$\longrightarrow \: \displaystyle \rm y = \int\limits_{ \sqrt{2} }^{ 5 \sqrt{2} } r \, dr$

$\longrightarrow \: \displaystyle \rm y = \Bigg[ \dfrac{ {r}^{2} }{2} \Bigg]_{ \sqrt{2} }^{ 5\sqrt{2} }$

$\longrightarrow \: \displaystyle \rm y = \dfrac{ {(5 \sqrt{2} )}^{2} }{2} - \dfrac{ {(\sqrt{2} )}^{2} }{2}$

$\longrightarrow \: \displaystyle \rm y = \dfrac{ 25 \times 2 }{2} - \dfrac{2}{2}$

$\longrightarrow \: \displaystyle \rm y = \dfrac{ 50 }{2} - \dfrac{2 }{2}$

$\longrightarrow \: \displaystyle \rm y = \dfrac{ 50 - 2}{2}$

$\longrightarrow \: \displaystyle \rm y = \dfrac{ 48}{2}$

$\longrightarrow \: \displaystyle \underline{ \underline{\rm y = 24}}$

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$\longrightarrow \: \displaystyle \rm y = \int\limits_{ 0 }^{1 } {e}^{x} \, dx$

$\longrightarrow \: \displaystyle \rm y = \Bigg[ {e}^{x} \Bigg]_{ 0 }^{ 1 }$

$\longrightarrow \: \displaystyle \rm y ={e}^{1} - {e}^{0}$

$\longrightarrow \: \displaystyle \rm y =e- 1$

$\longrightarrow \: \displaystyle \rm y =2.718- 1$

$\longrightarrow \: \displaystyle \underline{ \underline{\rm y = 1.718}}$

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