Let f be a real valued continuous function defined on the positive real axis such that g(x)=∫₀ˣ t f(t) dt. If g(x³)=x⁶+x⁷, then value of Σ r=1 ¹⁵ f(r³) is:

Integral Calculus: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q83

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let

f

be a real valued continuous function defined on the positive real axis such that

g(x)=\int_{0}^{x} t f(t) \, dt

. If

g(x^3)=x^6+x^7

, then value of

\sum_{r=1}^{15} f(r^3)

is:

JEE Main 2025 Integral Calculus Question with Solution (January Unspecified (session-level dataset), Q83) | JEE Arc

JEE Main 2025 · January, Unspecified (session-level dataset) · Q83

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let

f

be a real valued continuous function defined on the positive real axis such that

g(x)=\int_{0}^{x} t f(t) \, dt

. If

g(x^3)=x^6+x^7

, then value of

\sum_{r=1}^{15} f(r^3)

is: