Question
Let f( ) denote the area of the region in the first quadrant bounded by x=0, x=1, y^ 2 =x and y=| x-5|-|1- x|+ x^ 2 . Then (f(0)+f(1)) is equal to
JEE Main
Mathematics
Area Under Curves
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 12
- B. 14
- C. 7
- D. 9
Answer
C. 7
Step-by-step solution
For = 0: curve is y = 5 - 1 = 4 (horizontal line), area = _0^1 (4 - x ) dx = 4 - 2 3 = 10 3 For = 1 and 0 x 1: |x-5| = 5-x, |1-x| = 1-x, so y = 4 + x^2 Area = _0^1 (4 + x^2 - x ) dx = 4 + 1 3 - 2 3 = 11 3 f(0) + f(1) = 10 3 + 11 3 = 7
Related: Mathematics — Area Under Curves · All PYQ Banks