Evaluate the following definite integral
$integral subscript 0 superscript 4 open parentheses straight x plus straight x to the power of 3 over 2 end exponent close parentheses dx$

Solution

Let I = $integral subscript 0 superscript 4 space open parentheses straight x plus straight x to the power of 3 over 3 end exponent close parentheses dx space equals space open square brackets straight x squared over 2 plus fraction numerator straight x to the power of begin display style 5 over 2 end style end exponent over denominator begin display style 5 over 2 end style end fraction close square brackets subscript 0 superscript 4 space space space$
$space equals space open square brackets straight x squared over 2 plus 2 over 5 straight x to the power of 5 over 2 end exponent close square brackets subscript 0 superscript 4 space equals space open parentheses 16 over 2 plus 2 over 5 cross times 4 to the power of 5 over 2 end exponent close parentheses space minus space left parenthesis 0 plus 0 right parenthesis space equals space 8 plus 2 over 5 cross times 32 space equals space 8 plus 64 over 5 space equals space 104 over 5$

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Integrals

Evaluate the following definite integral
$integral subscript 0 superscript 4 open parentheses straight x plus straight x to the power of 3 over 2 end exponent close parentheses dx$

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