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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let f(x) and g(x) be two derivable function on R (the set of all real numbers) satisfying f(x)= x^3 2 +1-x ₀^x g(t) d t and g(x)=x- ₀^1 f^ (t) d t , then:

Options

  1. A₀^1 f(t) d t= 3 2
  2. B₀^1 f(t) d t= 5 4
  3. Cnumber of points of non-derivability of f(|x|) is zero
  4. Dnumber of points of non-derivability of f(|x|) is one

Correct answer

C. number of points of non-derivability of f(|x|) is zero

Step-by-step solution

Let k= ₀^1 f(t) d t array ll & g(x)=x-k & f(x)= x^3 2 +1-x ₀^x(t-k) d t= x^3 2 +1-x ( x^2 2 -k x )=1+k x^2 & k= ₀^1 f(t) d t= (t+ k t^3 3 )₀^1 k=1+ k 3 k= 3 2 & f(x)=1+ 3 x^2 2 array f(|x|)=1+ 3 x^2 2 which is always derivable.

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