Question

Good Morining!

What is ∫√x dx ?

plz give answere

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Answer 1

Answer:

good morning dear ❣️❣️

integration √x

integration x^1/2

(x^1/2+1)/1/2+1

2x³/²/3

this is your answer ❣️❣️✌️✌️

Answer 2

Answer:

$\implies \frac{2}{3} x \sqrt{x} + c \: \\ or \: \\ \implies \: \frac{2}{3} {x}^{ (\frac{3}{2} )} + c$

Step-by-step explanation:

Solution

According to the question,

$let \: i \: = \int \: \sqrt{x} \: dx \\ \\ \because \: \sqrt{y} = {y}^{ (\frac{1}{2}) } \\ \therefore \\ \\ i \: = \int \: {x}^{( \frac{1}{2}) } \: dx$

We know that,

$\int \: {x}^{n} \: dx = \frac{ {x}^{n + 1} }{n + 1} + c \: \\ \\ c \: is \: a \: constant \:$

Therefore

$i \: = \frac{ {x}^{ (\frac{1}{2} + 1)} }{ \frac{1}{2} + 1} + c \\ \\ i \: = \frac{ {x}^{( \frac{3}{2}) } }{ \frac{3}{2} } + c\\ \\ i \: = \frac{2}{3} {x}^{( \frac{3}{2} )} + c \\ \\ or \: \\ \\ i \: = \frac{2}{3} x \sqrt{x} + c \\ \\ \because \: {n}^{ \frac{3}{2} } = {n}^{1} \: {n}^{ \frac{1}{2} } = n \sqrt{n}$

Hope it helps you.