Math, asked by Mister360, 3 months ago

Solve
\bf\displaystyle \int^4_2\frac{\sqrt{x} }{\sqrt{6 - x + x} } dx


hukam0685: is your question typed correctly

Answers

Answered by Anonymous
43

Answer:

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Answered by hukam0685
11

Step-by-step explanation:

Given:

\bf\displaystyle \int^4_2\frac{\sqrt{x} }{\sqrt{6 - x + x} } dx

To find : Integral

Explanation:

\bf\displaystyle \int^4_2\frac{\sqrt{x} }{\sqrt{6 } } dx

\bf\displaystyle \frac{1}{\sqrt{6 } }\int^4_2\sqrt{x} dx

Do integration

 \int {x}^{n} dx =  \frac{ {x}^{n + 1} }{n + 1}  + c \\  \\

=\bf\displaystyle\frac{2}{\sqrt{6} } [\frac{x^{\frac{3}{2}}}{3}]

put lower and upper limits

  = \frac{2}{ \sqrt{6} } ( \frac{4 \times 2}{3}  -  \frac{2 \sqrt{2} }{3} ) \\  \\  =  \frac{2}{3 \sqrt{6} } (8 -  2\sqrt{2} ) \\  \\

or

  = \frac{2}{ \sqrt{6} } ( \frac{4 \times 2}{3}  -  \frac{2 \sqrt{2} }{3} ) \\  \\  =  \frac{4}{3 \sqrt{6} } (4 - \sqrt{2} ) \\  \\

Thus,

\bf\displaystyle \int^4_2\frac{\sqrt{x} }{\sqrt{6 - x + x} } dx=\frac{4}{3 \sqrt{6} } (4 - \sqrt{2} )

Hope it helps you.

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