Question

class12 ..integration
step by step.​

Answer 1

Step by step explaination

see the attachment

Answer 2

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ᴀɴsᴡᴇʀ :

$\red \bigstar \: \boxed{\tt\int|x|dx =\dfrac{x|x|}{2}+C}$

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ɢɪᴠᴇɴ ǫᴜᴇsᴛɪᴏɴ :

$\implies \sf\int |x|dx$

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sᴛᴇᴘ ʙʏ sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ :

$\sf{{Integrate\:by \:parts:} \tt{\int fg' = fg-\int f'g}}$

$\implies\tt{f =|x|},\:\:g'=1$

$\implies\tt{f'= \dfrac{x}{|x|} \: ,g =x:}$

$\tt\implies=x|x| - \int |x|dx$

The integral $\tt\int |x|dx$ appears again on the right side of the equation, we can solve for it :

$\tt \implies\:\dfrac{x|x| }{2}$

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The problem is solved :

$\tt\implies\int|x|dx =\dfrac{x|x|}{2}+C$

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