AP EAMCET · Maths · Definite Integration
\(\int_1^5(|x-3|+|1-x|) d x=\)
- A 4
- B 8
- C 12
- D 24
Answer & Solution
Correct Answer
(C) 12
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }|x-3|= \begin{cases}3-x, & x \lt 3 \\ x-3, & x\gt3\end{cases} \\ & \text { and }|1-x|=x-1 ; x\gt1 \\ & I=\int_1^5(|x-3|+|1-x|) d x \\ & =\int_1^3(3-x+x-1) d x+\int_3^5(x-3+x-1) d x \\ & =\int_1^3 2 d x+\int_3^5(2 x-4) d x=4+\left[x^2-4 x\right]_3^5=12…
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