Question
The area bounded by the curves x+2 y^ 2 =0 and x+3 y^ 2 =1 is
BITSAT
Mathematics
Area Under Curves
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. 1 sq. unit
- B. 1 3 sq. units
- C. 2 3 sq. units
- D. 4 3 sq. units
Answer
D. 4 3 sq. units
Step-by-step solution
We have, x+2 y^ 2 =0 y^ 2 =- x 2 (i) a parabola with vertex (0,0) and x+3 y^ 2 =1 y^ 2 = 1-x 3 =- ( x-1 3 ) (ii), a parabola with vertex (1,0) Solving (i) and (ii), we get y= 1 A = _ -1 ^ 1 ( (1-3 y^ 2 )- (-2 y^ 2 ) ) d y =2 _ 0 ^ 1 (1-y^ 2 ) d y=2 [y- y^ 3 3 ]_ 0 ^ 1 = 4 3 sq.units
Related: Mathematics — Area Under Curves · All PYQ Banks