If for a continuous function f(x), _ - ^ t (f(x) + x)dx = ^2 - t^2, for all t - , then f (- 3 ) is equal to:

JEE Main 2014 Mathematics question

If for a continuous function f(x), , for all , then is equal to:

Answer: (1)

Differentiating both sides with respect to t (the integrand is continuous, so the fundamental theorem applies):

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Question ID VK-104609