Question
The area enclosed by the curves y= x+ x and y=| x- x| over the interval [0, 2 ] is
BITSAT
Mathematics
Area Under Curves
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 4( 2 -1)
- B. 2 2 ( 2 -1)
- C. 2( 2 +1)
- D. 2 2 ( 2 +1)
Answer
B. 2 2 ( 2 -1)
Step-by-step solution
Given, y= x+ x, x [0, / 2] d y d x = x- x aligned y & =| x- x| \\ & = [ array cc x- x & x [0, / 4] \\ x- x & x [ / 4, / 2] array ] aligned Required area aligned &= _0^ / 4 |( x+ x)-( x- x)| d x+ _ / 4 ^ / 2 |2 x| d x aligned = _0^ / 4 |2 x| d x+ _ / 4 ^ / 2 |2 x| d x =2(- x)_0^ / 4 +2( x)_ / 4 ^ / 2 =2 [- 1 2 +1+1- 1 2 ] aligned = & 2 (2- 2 2 ) \\ = & 2(2- 2 ) \\ = & 4-2 2 \\ = & 2 2 ( 2 -1) aligned
Related: Mathematics — Area Under Curves · All PYQ Banks