Let a differentiable function f satisfy the equation \int_{0}^{36} f (\frac{t x}{36}) \dt=4 \alpha f(x). If y=f(x) is a standard parabola passing through the points (2,1) and (-4, \beta), then \beta^\alpha is equal to \_\_\_\_。 [24 jan 2026 Shift 1]

Definite Integrals Part 3

Section: Mathematics

Question : 6 of 115

Marks: +1, -0

Let a differentiable function f satisfy the equation

∫

f(‌

)‌dt=4αf(x). If y=f(x) is a standard parabola passing through the points (2,1) and (−4,β), then βα is equal to ____。

[24 jan 2026 Shift 1]

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