Evaluate the following definite integral using the Fundamental Theorem of Calculus. \( \frac{1}{10} \int_{0}^{\ln 2} e^{x} d x \) \( \frac{1}{10} \int_{0}^{\ln 2} e^{x} d x=\square \) (Type an integer or a simplified fraction.)

To evaluate the integral \( \frac{1}{10} \int_{0}^{\ln 2} e^{x} d x \), we first need to solve the integral \( \int e^{x} d x \), which is simply \( e^{x} + C \). Now, applying the Fundamental Theorem of Calculus: \[ \int_{0}^{\ln 2} e^{x} d x = \left[ e^{x} \right]_{0}^{\ln 2} = e^{\ln 2} - e^{0} = 2 - 1 = 1. \] Now, we multiply this result by \( \frac{1}{10} \): \[ \frac{1}{10} \int_{0}^{\ln 2} e^{x} d x = \frac{1}{10} \cdot 1 = \frac{1}{10}. \] So the final answer is \[ \frac{1}{10}. \] Hence \( \frac{1}{10} \int_{0}^{\ln 2} e^{x} d x=\frac{1}{10} \).