Question
The area of the region A = \ (x, y): 4 x^ 2 +y^ 2 8 . and .y^ 2 4 x \ is:
JEE Main
Mathematics
Area Under Curves
2026
JEE Main 2026 (22 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. +4
- B. + 2 3
- C. 2 +2
- D. 2 + 1 3
Answer
B. + 2 3
Step-by-step solution
A = _ 0 ^ 2 2 x \, dx + 2 _ 1 ^ 2 8 - 4x^2 \, dx = 8 3 ( x^ 3 2 ) |_ 0 ^ 1 + 4 _ 1 ^ 2 2 - x^2 \, dx = 8 3 + 4 1 2 [ x 2 - x^2 + 2 ^ -1 ( x 2 ) ] |_ 1 ^ 2 = 8 3 + 2 [ 2 2 - 1 - 2 4 ] = 8 3 + 2 - 2 - = + 2 3 sq. units
Related: Mathematics — Area Under Curves · All PYQ Banks