Integral Example - # 5

[Jason76]

Definite Integral with top at 3 and bottom at -2

\(\displaystyle \int (x^{3} - 4x) dx \)

\(\displaystyle \rightarrow \dfrac{x^{4}}{4} - \dfrac{4x^{2}}{2}\)

\(\displaystyle \rightarrow \dfrac{x^{4}}{4} - 2x^{2}\)

\(\displaystyle [\dfrac{(3)^{4}}{4} - 2(3)^{2}] - [\dfrac{(-2^{4}}{4} - 2(-2)^{2}]\)

\(\displaystyle \dfrac{81}{4} - 18] - [-\dfrac{16}{4} - 8]\)

\(\displaystyle [\dfrac{81}{4} - 18] + [\dfrac{16}{4} - 8]\)

\(\displaystyle [\dfrac{81}{4} - \dfrac{72}{4}] + [\dfrac{16}{4} -\dfrac{32}{4}]\)

\(\displaystyle [\dfrac{9}{4}] + [-\dfrac{16}{4}\)

\(\displaystyle [\dfrac{9}{4}] - [\dfrac{16}{4}] = -\dfrac{7}{4}\) - The computer says answer is wrong.

 

[stapel]

Formatting and lingo is corrected....

\(\displaystyle \displaystyle{\int_{-2}^3\, \left(x^3\, -\, 4x\right)\, dx}\)

\(\displaystyle \Rightarrow \left.\dfrac{x^{4}}{4}\, -\, \dfrac{4x^{2}}{2}\right|_{-2}^3\)

\(\displaystyle =\, \left.\dfrac{x^{4}}{4}\, -\, 2x^{2}\right|_{-2}^3\)

\(\displaystyle =\,\left[\dfrac{(3)^{4}}{4}\, -\, 2(3)^{2}\right]\, -\, \left[\dfrac{(-2)^{4}}{4}\, -\, 2(-2)^{2}\right]\)

\(\displaystyle =\,\left[\dfrac{81}{4}\, -\, 18\right]\, -\, \left[-\dfrac{16}{4}\, -\, 8\right]\)

No; (-2)^4 is not equal to -16.

 

[Jason76]

Definite Integral with top at 3 and bottom at -2

\(\displaystyle \int (x^{3} - 4x) dx \)

\(\displaystyle \rightarrow \dfrac{x^{4}}{4} - \dfrac{4x^{2}}{2}\)

\(\displaystyle \rightarrow \dfrac{x^{4}}{4} - 2x^{2}\)

\(\displaystyle [\dfrac{(3)^{4}}{4} - 2(3)^{2}] - [\dfrac{(-2^{4}}{4} - 2(-2)^{2}]\)

\(\displaystyle \dfrac{81}{4} - 18] - [\dfrac{16}{4} - 8]\) Correction made.

\(\displaystyle [\dfrac{81}{4} - 18] - [\dfrac{16}{4} - 8]\)

\(\displaystyle [\dfrac{81}{4} - \dfrac{72}{4}] - [\dfrac{16}{4} -\dfrac{32}{4}]\)

\(\displaystyle [\dfrac{9}{4}] - [-\dfrac{16}{4}\)

\(\displaystyle [\dfrac{9}{4}] + [\dfrac{16}{4}] = \dfrac{25}{4}\) - Correct on computer.

But computer wanted decimal answer of 6.25.

 

[stapel]

\(\displaystyle [\dfrac{9}{4}] + [\dfrac{16}{4}] = \dfrac{25}{4}\) - Correct on computer.

But computer wanted decimal answer of 6.25.

So... what is your question? :wink: