Definite integral question

[Guest]

If the definitie integral of 3x^2 - 2x dx = 100 for x = 0 and x =a.

Then find a...

Well my working out would be

3 x integral of x^2 - 2 times the integral of x dx =
x^3 - x^2 = 100 for x = 0 and and x=a

ie.

a^3 - a^2 = 100
my answer is a^2(a-1) = 100
thus either a = 10 or a = 101

Is this correct?

 

[galactus]

Put your answer into the integral and see if it's correct.

\(\displaystyle \L\\\int(3x^{2}-2x)dx=x^{3}-x^{2}\)

\(\displaystyle \L\\10^{3}-10^{2}=900\)...Oops!

\(\displaystyle \L\\101^{3}-101^{2}=1020100\)...Oops!

Try again.

 

[pka]

Have you forgotten how to use basic algebra?
\(\displaystyle \L a^3 - a^2 = 100\quad \Rightarrow \quad a^3 - a^2 - 100 = 0\).

Try \(\displaystyle a = 5\).

 

[Guest]

Big oops! he he he

You are correct!

 

[stapel]

3 x integral of x^2 - 2 times the integral of x dx

The above means one of the following:

. . . . .\(\displaystyle \L \left[3x\,\int{\left(x^2\,-\,2 \right)}\right]\, \left[\int{x}dx\right]\)

. . . . .\(\displaystyle \L \left[3x\,\int{x^2}\right]\,-\,\left[2\, \int{x}dx\right]\)

Is either of these what you meant? If so, which? How did you arrive at this? What does it mean? If not, what did you mean?

Thank you.

Eliz.