Definite Integration
Definite Integration
nta_pyq_2025_jan
Grade 12
Question:
Let f (x) = \int x 0 t -8t+15 t dt, x \in R . Then the numbers of local maximum and local minimum points of f , e respectively, are :
2 and 3
2 and 2
3 and 2
1 and 3
Step-by-Step Solution
Key Concept: Apply the core result for definite integral properties and simplify using the given constraints.
2 x 2 t - 8t + 15 f (x) = \int dt, x \in R (1) 0 e t 4 2 x - 8x + 15 ′ f (x) = (2x) = 0 2 x e 2 2 2 \times (x - 5) (x - 3) \Rightarrow = 0 2 x e \Rightarrow x(x + \sqrt5)(x - \sqrt5)(x + \sqrt3)(x - \sqrt3) = 0 By using wavy curve method Number of local maximum = 2 Number of local minimum = 3 x
Correct Answer: 1