Evaluate the following definite integral
$integral subscript 0 superscript 4 straight x to the power of 1 half end exponent dx$

Solution

Let I = $integral subscript 0 superscript 4 straight x to the power of 1 half end exponent dx space equals space open square brackets fraction numerator straight x to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close square brackets subscript 0 superscript 4 space equals space 2 over 3 open square brackets straight x to the power of 3 over 2 end exponent close square brackets subscript 0 superscript 4 space equals space 2 over 3 open square brackets 4 to the power of 3 over 2 end exponent minus 0 close square brackets space equals space 2 over 3 cross times left parenthesis 2 cubed minus 0 right parenthesis space equals space 2 over 3 cross times 8 space equals space 16 over 3$

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Integrals

Evaluate the following definite integral
$integral subscript 0 superscript 4 straight x to the power of 1 half end exponent dx$

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