- #1

rxh140630

- 60

- 11

- Homework Statement:
- Find all x>0 for which $$\int_0^x [t]^{2} dt = 2(x-1) $$

- Relevant Equations:
- The notation [x] denotes the greatest integer less than or equal to x

In the question above it, the author (Apostol) states: $$\int_0^n [t]^{2} dt = \frac{n(n-1)(2n-1)}{6}$$

Why can't I set the two equations = and get the result?

2(x-1) = x(x-1)(2x-1)/6 => 12 = 2x^2 - x => 0 = x^2-(x/2) -6

using quadratic equation I get the wrong answer

Why can't I set the two equations = and get the result?

2(x-1) = x(x-1)(2x-1)/6 => 12 = 2x^2 - x => 0 = x^2-(x/2) -6

using quadratic equation I get the wrong answer