Find the area under the curve of 
between 
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=4}
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| Foundations:
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| For solving the problem, we only require the use of the power rule for integration:
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| For setup of the problem we need to integrate the region between the x - axis, the curve, x = 1, and x = 4.
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Solution:
| Step 1:
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| Set up the integral:
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_1^{\,4} \frac{8}{\sqrt{x}} \,dx.}
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| Step 2:
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| Using the power rule we have:
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- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{array}{rcl}\displaystyle {\int _{1}^{\,4}{\frac {8}{\sqrt {x}}}\,dx}&=&\displaystyle {\int _{1}^{\,4}8x^{-1/2}\,dx}\\\\&=&\displaystyle {{\frac {8x^{1/2}}{2}}{\Bigr |}_{x=1}^{4}}\\\\&=&4x^{1/2}{\Bigr |}_{x=1}^{4}.\end{array}}}
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| Step 3:
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| Now we need to evaluate to get:
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4x^{1/2} \Bigr|_{x=1}^4\,=\,4\cdot 4^{1/2} - 4\cdot 1^{1/2} \,=\, 8 - 4 \,=\, 4.}
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| Final Answer:
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_1^{\,4} \frac{8}{\sqrt{x}} \,dx\,=\,4.}
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