Definite Integration Question 290
Question: If $ f(x)= \begin{cases} 4x+3, & if & 1\le x\le 2 \\ 3x+5, & if & 2<x\le 4 \\ \end{cases} . $ then $ \int_1^{4}{f(x)}dx= $
Options:
A) 80
B) 20
C) $ -20 $
D) 37
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int_1^{4}{f(x)dx=\int_1^{2}{(4x+3)dx+\int_2^{4}{(3x+5)dx}}} $
$ =| 2x^{2}+3x |_1^{2}+| \frac{3x^{2}}{2}+5x |_2^{4}=37 $ .
BETA
