Definite Integration Problem - # 3

[Jason76]

\(\displaystyle \int^{4}_{0} 2x^{3} - 4x - 6\)

\(\displaystyle \int^{4}_{0}\dfrac{x^{4}}{2} - 2x^{2} - 6x\)

\(\displaystyle \rightarrow [\dfrac{(4)^{4}}{2} - 2(4)^{2} - 6(4)] - [0]\) Other side evaluates to \(\displaystyle 0\)

\(\displaystyle 2 - 32 - 24 = -54\) Computer says this is wrong

 

[Deleted member 4993]

\(\displaystyle \int^{4}_{0} 2x^{3} - 4x - 6\)

\(\displaystyle \int^{4}_{0}\dfrac{x^{4}}{2} - 2x^{2} - 6x\)

\(\displaystyle \rightarrow [\dfrac{(4)^{4}}{2} - 2(4)^{2} - 6(4)] - [0]\) Other side evaluates to \(\displaystyle 0\)

\(\displaystyle 2 - 32 - 24 = -54\) Computer says this is wrong

\(\displaystyle \rightarrow [\dfrac{(4)^{4}}{2} - 2(4)^{2} - 6(4)] - [0]\)

= 256/2 - 32 - 24 = ????

 

[lookagain]

\(\displaystyle \int^{4}_{0} (2x^{3} - 4x - 6)dx \ \ \ \) Put grouping symbols and your dx in there.

\(\displaystyle \int^{4}_{0}\dfrac{x^{4}}{2} - 2x^{2} - 6x \ \ \ \)No, drop the integration symbol, and instead place a vertical bar at the right with the integration limits.

\(\displaystyle \rightarrow [\dfrac{(4)^{4}}{2} - 2(4)^{2} - 6(4)] - [0]\) Other side evaluates to \(\displaystyle 0\)

\(\displaystyle 2 - 32 - 24 = -54\) Computer says this is wrong

\(\displaystyle \bigg(\dfrac{x^{4}}{2} - 2x^{2} - 6x\bigg) \ \bigg|_0^4\ \ \ \)


\(\displaystyle This \ \ portion: \ \ \dfrac{4^4}{2} \ = \ \dfrac{256}{2} \ = \ 128\)

 

[Jason76]

\(\displaystyle \bigg(\dfrac{x^{4}}{2} - 2x^{2} - 6x\bigg) \ \bigg|_0^4\ \ \ \)


\(\displaystyle This \ \ portion: \ \ \dfrac{4^4}{2} \ = \ \dfrac{256}{2} \ = \ 128\)

Sorry, it's still wrong. I don't know what the problem is.

 

[Bob Brown MSEE]

Does your computer say 72?

Sorry, it's still wrong. I don't know what the problem is.

Click Here

 

[mr_lee]

mr_lee

\(\displaystyle \int^{4}_{0} 2x^{3} - 4x - 6\)

\(\displaystyle \int^{4}_{0}\dfrac{x^{4}}{2} - 2x^{2} - 6x\)

\(\displaystyle \rightarrow [\dfrac{(4)^{4}}{2} - 2(4)^{2} - 6(4)] - [0]\) Other side evaluates to \(\displaystyle 0\)

\(\displaystyle 2 - 32 - 24 = -54\) Computer says this is wrong

answer: 256/2 - 32 - 24 = 128 - 32 -24 = 72

 

[HallsofIvy]

Frankly, it is hard to believe that this was not a joke. You know, do you not, that \(\displaystyle 4^2= 16\)? So how could you think that \(\displaystyle 4^4= 4\)?