Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x) + g(x) = x². Then the value of the integral ∫₀¹ f(x)g(x)dx, is

Integral Calculus: JEE Main 2003 Mathematics question

JEE Main 2003 · Annual, Paper 1 · Q3331

JEE Main 2003Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

Let

f(x)

be a function satisfying

f'(x)=f(x)

with

f(0)=1

and

g(x)

be a function that satisfies

f\left( x \right) + g\left( x \right) = {x^2}

. Then the value of the integral

\int\limits_0^1 {f\left( x \right)g\left( x \right)dx,}