Question

intigration of 2/ root x​

Answer 1

Step-by-step explanation:

refer the attachment

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Answer 2

★given:-

$\implies \red{ \frac{2}{ \sqrt{x} } }$

★find:-

$\implies \int \: \frac{2}{ \sqrt{x} } dx = {?}^{}$

★solution:-

$\implies \int \: \frac{2}{ \sqrt{x} }dx$

we know that formula of

$\implies \star \pink{ \int \: x .\: dx = \frac{x {}^{n + 1} }{n + 1} }$

can we be written as

$\implies \int \: \frac{2}{x {}^{ \frac{1}{2} } }dx$

$\implies \int \: 2x {}^{ - \frac{1}{2} } dx$

applie formula

2 constant term so out of int

$\implies \:2 \int \frac{x {}^{1 + (- \frac{1}{2}) } }{1 + ( - \frac{1}{2}) } \\ \\ \implies2 \: \frac{x {}^{1 - \frac{1}{2} } }{1 - \frac{1}{2} } \\ \\ \implies 2 \: \frac{x { }^{ {}^{ \frac{1}{2} } } }{ \frac{1}{2} } \\ \\ \implies 2 \times 2 \sqrt{x} \: \\ \\ \implies \: 4 \sqrt{x}+C$

answer

$\implies \pink{ \int \: \frac{2}{ \sqrt{x} } dx = 4 \sqrt{x}+C }$

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