Let f(x)+2f (1/x)=x²+5 and 2g(x)-3g (1/x)=x, x>0. If α=∫₁² f(x) dx and β=∫₁² g(x) dx, then the value of 9α+β is:

Integral Calculus: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q118

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

Let

f(x)+2f\bigl(\tfrac{1}{x}\bigr)=x^2+5

and

2g(x)-3g\bigl(\tfrac{1}{x}\bigr)=x

x>0

. If

\alpha=\int_1^2 f(x)\,dx

and

\beta=\int_1^2 g(x)\,dx

, then the value of

9\alpha+\beta

is:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q118

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

Let

f(x)+2f\bigl(\tfrac{1}{x}\bigr)=x^2+5

and

2g(x)-3g\bigl(\tfrac{1}{x}\bigr)=x

x>0

. If

\alpha=\int_1^2 f(x)\,dx

and

\beta=\int_1^2 g(x)\,dx

, then the value of

9\alpha+\beta

is: