Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let f(x)= _ -1 ^1(1-|t|) (x t) d t then which of the following hold true?

Options

Af(0) is not defined
BLim _ x 0 f(x) exists and equals 2
CLim _ x 0 f(x) exists and is equal to 1
Df(x) is continuous at x=0

Correct answer

D. f(x) is continuous at x=0

Step-by-step solution

f(x)=2 ₀^1 (1-t) _I (x t) _ I I d t=2 [ .(1-t) x t x |₀ ^1+ 1 x ₀^1 x t d t ]=2 [0- . 1 x^2 x t |₀ ^1 ]f(x)=2 [ 1- x x^2 ](x 0) if x=0 then f(x)= _ -1 ^1(1-|t|) d t=2 ₀^1(1-t) d t=1 (C) is correct hence f(x)= [ array c 2 ( 1- x x^2 ) if x 0 1 1 array . f is continuous at x =0 (D) is correct

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