Question
Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ]. Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?
NDA
Mathematics
Area Under Curves
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. k
- B. 1-k
- C. ( -k) 2
- D. ( -2k) 2
Answer
B. 1-k
Step-by-step solution
Given k = _ 0 ^ /4 x \, dx k = [- x]_ 0 ^ /4 = - ( 4 ) + (0) = 1 - 1 2 The required area is A = _ /4 ^ /2 x \, dx A = [- x]_ /4 ^ /2 = - ( 2 ) + ( 4 ) = 1 2 From the expression for k, we have 1 2 = 1 - k Therefore, A = 1 - k Answer: 1-k
Related: Mathematics — Area Under Curves · All PYQ Banks