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
A. k
Step-by-step solution
k = _ 0 ^ /4 x \, dx Let the required area be A = _ /4 ^ /2 x \, dx Substituting x = 2 - t, we get dx = -dt When x = 4 , t = 4 and when x = 2 , t = 0 A = _ /4 ^ 0 ( 2 - t ) (-dt) A = _ 0 ^ /4 t \, dt A = k Answer: k
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