Definite Integral Problem

[Jason76]

\(\displaystyle \int^{1}_{0} 3 + \dfrac{1}{4}x^{4} - \dfrac{4}{5}x^{9} dx\)

\(\displaystyle \rightarrow 3x + (\dfrac{1}{4}) \dfrac{x^{5}}{5} - (\dfrac{4}{5})\dfrac{x^{10}}{10} \)

\(\displaystyle \rightarrow 3x + \dfrac{x^{5}}{20} - \dfrac{4x^{10}}{50} \)

 

[DrPhil]

\(\displaystyle \int^{1}_{0} 3 + \dfrac{1}{4}x^{4} - \dfrac{4}{5}x^{9} dx\)

\(\displaystyle \rightarrow 3x + (\dfrac{1}{4})\dfrac{x^{5}}{5} - (\dfrac{4}{5})\dfrac{x^{10}}{10} \)

\(\displaystyle \rightarrow 3x + (\dfrac{1}{4})\dfrac{x^{5}}{20} - \dfrac{4x^{10}}{50} \)

\(\displaystyle \displaystyle \left.\left(3x + (\dfrac{1}{4})\dfrac{x^{5}}{5} - \dfrac{4x^{10}}{50}\right) \right|_0^1 \)

Evaluate at x=1 and at x=0, and subtract.