AP EAMCET202119 Aug 2021Morning ShiftMathematicsDefinite IntegrationActual
∫ 2 4   | x − 2 | + | x − 3 | d x =
Options
- A1
- B2
- C3
- D4
Correct answer
C. 3
Step-by-step solution
Given that ∫ 2 4   | x − 2 | + | x − 3 | d x If x     >   2   ⇒ x - 2   =   x - 2 . If 2 < x < 3   ⇒ x - 3   =   3 - x   &   3 < x < 4   ⇒ x - 3   =   x - 3 =   ∫ 2 4 x - 2 d x   +   ∫ 2 3 3 - x d x   +   ∫ 3 4 x - 3 d x =   x 2 2 - 2 x 2 4   +   3 x - x 2 2 2 3   +   x 2 2 - 3 x 3 4   = 2 - 1 2 + 1 2 = 3