1. **State the problem:** We want to approximate the area under the curve $f(x) = x^2$ on the interval $[0,1]$ using the left Riemann sum with $n=4$ subintervals. 2. **Formula and explanation:** The left Riemann sum is given by $$L_n = \sum_{i=0}^{n-1} f(x_i) \Delta x$$ where $\Delta x = \frac{b-a}{n}$ is the width of each subinterval, and $x_i = a + i \Delta x$ are the left endpoints. 3. **Calculate $\Delta x$:** $$\Delta x = \frac{1-0}{4} = 0.25$$ 4. **Find the left endpoints:** $$x_0 = 0, \quad x_1 = 0.25, \quad x_2 = 0.5, \quad x_3 = 0.75$$ 5. **Evaluate $f(x_i)$ at each left endpoint:** $$f(0) = 0^2 = 0$$ $$f(0.25) = (0.25)^2 = 0.0625$$ $$f(0.5) = (0.5)^2 = 0.25$$ $$f(0.75) = (0.75)^2 = 0.5625$$ 6. **Compute the left Riemann sum:** $$L_4 = \Delta x \times \left(f(0) + f(0.25) + f(0.5) + f(0.75)\right) = 0.25 \times (0 + 0.0625 + 0.25 + 0.5625)$$ $$L_4 = 0.25 \times 0.875 = 0.21875$$ **Final answer:** The left Riemann sum approximation of the area under $f(x) = x^2$ on $[0,1]$ with 4 subintervals is $0.21875$.