If a continuous function \( f \) satisfies \( \int_{0}^{f(x)} t^{2} d t \) \( =x^{2}(1+x) \) for... VIDEO
If a continuous function \( f \) satisfies \( \int_{0}^{f(x)} t^{2} d t \) \( =x^{2}(1+x) \) for all \( x \geq 0 \) then \( f(2) \) is equal to
(a) 12
(b) \( \sqrt[3]{36} \)
(c) 3
(d) \( \sqrt[3]{42} \)
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