Definite Integration
General
Grade 12
Question:
Evaluate $\int_{-3}^{5} e^{\{x\}} dx$, where $\{.\}$ denotes the fractional part function.
Step-by-Step Solution
Key Concept: General
$\int_{-3}^{5} e^{\{x\}} dx = (5 - (-3)) \int_{0}^{1} e^{\{x\}} dx = 8 \int_{0}^{1} e^x dx = 8(e^x)_0^1 = 8(e - 1)$
Correct Answer: 8(e - 1)