Let $I_1 = \int_0^e x^2dx$ and $I_2 = \int_0^e 2x e^x dx$, then the value of $I_1 + I_2$ is equal to
Step-by-Step Solution
Key Concept: Definite integration represents the area under a curve, which can be computed using geometric formulas for simple shapes.
The shaded area under the curve $f(x)$ is calculated using the formula for the area of a trapezoid: $\int f(x)dx = \text{shaded area} = 2(\frac{1}{\text{base} \cdot \text{height}}) = 2(\frac{1}{2} \cdot 1 \cdot \frac{1}{2}) = \frac{1}{2}$. This represents the definite integral of the function over the given interval.
Correct Answer: C