Let is a real valued function defined by

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

Let

f(x)

is a real valued function defined by

f(x) = x^2 + x^2 \int_{-1}^{x} t f(t)\, dt + x^3 \int_{-1}^{x} f(t)\, dt

, then which of the following hold(s) good? (1)

\int_{-1}^{1} t f(t) dt = \frac{10}{11}

(2)

f(1) + f(-1) = \frac{30}{11}

(3)

\int_{-1}^{1} t f(t) dt > \int_{-1}^{1} f(t) dt

(4)

f(1) - f(-1) = \frac{20}{11}