Q.45 \int_{0}^{4}|2 x-5| \, dx =
A. \frac{13}{2}
B. \frac{15}{2}
C. \frac{17}{4}
D. \frac{17}{2}
Answer: D
Solution:
\int_{0}^{4}|2 x-5| \, dx = \int_{0}^{\frac{5}{2}}(5-2 x) \, dx + \int_{\frac{5}{2}}^{4}(2 x-5) \, dx = \left[ 5 x - x^2 \right]_{0}^{\frac{5}{2}} + \left[ x^2 - 5 x \right]_{\frac{5}{2}}^{4} = \frac{25}{4} + \frac{9}{4} = \frac{34}{4} = \frac{17}{2}