Definite Integration
Definite Integration
nta_pyq_2025_jan
Grade 12
Question:
Let f be a real valued continuous function defined on the positive real axis such that g(x) = \int . If x tf (t)dt 0 , then value of \sum is : 15 3 6 7 3 g (x ) = x + x f (r ) r=1
Step-by-Step Solution
Key Concept: Apply the core result for definite integral properties and simplify using the given constraints.
g(x) = x 2 + x 7/3 (4) ′ g (x) = 2x + 7 x 4/3 3 ′ g (x) f (x) = x 7 1/3 f (x) = 2 + x 3 7 3 f (r ) = 2 + r 3 15 7 7 15(16) \sum (2 + r) = 2(15) + ( ) 3 3 2 r=1 = 310
Correct Answer: 4