Question
Let the area of the region bounded by the curve y= \ x, x\ , lines x=0, x= 3 2 , and the x-axis be A. Then, A + A ^ 2 is equal to \_\_\_\_.
JEE Main
Mathematics
Area Under Curves
2026
JEE Main 2026 (23 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
A = _ 0 ^ /4 x \, dx + _ /4 ^ x \, dx + _ ^ 5 /4 - x \, dx + _ 5 /4 ^ 3 /2 - x \, dx A = ( x)_ 0 ^ /4 + (- x)_ /4 ^ + ( x)_ ^ 5 /4 + ( x)_ 5 /4 ^ 3 /2 A = 1 2 + 1 2 + 1 + 1 - 1 2 + 1 - 1 2 = 3 A^2 + A = 12
Related: Mathematics — Area Under Curves · All PYQ Banks