Question: User: \int_3^6 xdx
1. **State the problem:** Calculate the definite integral $$\int_3^6 x \, dx$$.
2. **Recall the formula:** The integral of $$x$$ with respect to $$x$$ is $$\frac{x^2}{2} + C$$, where $$C$$ is the constant of integration.
3. **Apply the definite integral formula:**
$$\int_a^b f(x) \, dx = F(b) - F(a)$$ where $$F(x)$$ is the antiderivative of $$f(x)$$.
4. **Find the antiderivative:**
$$F(x) = \frac{x^2}{2}$$.
5. **Evaluate at the limits:**
$$F(6) - F(3) = \frac{6^2}{2} - \frac{3^2}{2} = \frac{36}{2} - \frac{9}{2}$$.
6. **Simplify:**
$$\frac{36}{2} - \frac{9}{2} = \frac{36 - 9}{2} = \frac{27}{2}$$.
7. **Final answer:**
$$\int_3^6 x \, dx = \frac{27}{2} = 13.5$$.
This means the area under the curve $$y=x$$ from $$x=3$$ to $$x=6$$ is $$13.5$$.