# More Simpson Rule Question

#### Paymemoney

Hi

The following question i don't know why it is incorrect.
1)$$\displaystyle \int_1^3 x^{x}dx$$ n=4

$$\displaystyle x_0 = 0$$

$$\displaystyle x_1 = \frac{1}{4}$$

$$\displaystyle x_2 = \frac{2}{4}$$

$$\displaystyle x_3 = \frac{3}{4}$$

$$\displaystyle x_4 = \frac{4}{4}$$

$$\displaystyle \int_0^1 x^{x} dx = \frac{1}{12}[0+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\frac{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]$$

=0.70553

#### CaptainBlack

MHF Hall of Fame
Hi

The following question i don't know why it is incorrect.
1)$$\displaystyle \int_1^3 x^{x}dx$$ n=4

$$\displaystyle x_0 = 0$$

$$\displaystyle x_1 = \frac{1}{4}$$

$$\displaystyle x_2 = \frac{2}{4}$$

$$\displaystyle x_3 = \frac{3}{4}$$

$$\displaystyle x_4 = \frac{4}{4}$$

$$\displaystyle \int_0^1 x^{x} dx = \frac{1}{12}[0+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\frac{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]$$

=0.70553

Why have you used $$\displaystyle 0^0=0$$ in this case? You need $$\displaystyle \lim_{x \to 0}x^x=1$$

Next time you post a question try to make it clear what your question is, and don't change the detail part way through.

CB

#### Paymemoney

Hi

The following question i don't know why it is incorrect.
1)$$\displaystyle \int_0^1 x^{x}dx$$ n=4

$$\displaystyle x_0 = 0$$

$$\displaystyle x_1 = \frac{1}{4}$$

$$\displaystyle x_2 = \frac{2}{4}$$

$$\displaystyle x_3 = \frac{3}{4}$$

$$\displaystyle x_4 = \frac{4}{4}$$

$$\displaystyle \int_0^1 x^{x} dx = \frac{1}{12}[0+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\frac{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]$$

=0.70553

srry about that, the above is the correct equation.

#### CaptainBlack

MHF Hall of Fame
$$\displaystyle \int_0^1 x^{x} dx = \frac{1}{12}[1+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\frac{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]$$

=0.7889

#### Paymemoney

$$\displaystyle \int_0^1 x^{x} dx = \frac{1}{12}[1+4(\frac{1}{4}^{\frac{1}{4}})+2(\frac{1}{2}^{\frac{1}{2}})+4(\frac{3}{4}^{\frac{3}{4}})+1]$$

=0.7889
but isn't $$\displaystyle x_0$$ equal to 0?

#### CaptainBlack

MHF Hall of Fame
but isn't $$\displaystyle x_0$$ equal to 0?
No that's why I said it's not in post #2 in this thread. $$\displaystyle 0^0$$ is undefined here you need to use $$\displaystyle \lim_{x\to 0}x^x=1$$ for the value of the integrand at $$\displaystyle x=0$$

CB