Let f be a differentiable function satisfying f(x) = 1 - 2x + ∫₀ˣ e^((x-t)) f(t) dt, x R and let g(x) = ∫₀ˣ (f(t) + 2)¹⁵ (t-4)⁶ (t+12)¹⁷ dt, x R. If p and q are respectively the points of local minima and local maxima of g, then the value of |p + q| is equal to _ _ _ _.

Differential Equations: JEE Main 2026 Mathematics question

JEE Main 2026 · 28 Jan, Evening shift · Q24

JEE Main 202628 Jan, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let f be a differentiable function satisfying

f(x) = 1 - 2x + \int_0^x e^{(x-t)} f(t)\, dt

x \in \mathbb{R}

and let

g(x) = \int_0^x (f(t) + 2)^{15} (t-4)^6 (t+12)^{17}\, dt

x \in \mathbb{R}

. If p and q are respectively the points of local minima and local maxima of g, then the value of

|p + q|

is equal to ________.

Your answerType your answer. Integers and decimals are accepted.