_ h 0 _ a ^ x+h ^ 2 t d t- _ a ^ x ^ 2 t d t h equals to
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
\[\lim _{h \rightarrow 0} \frac{\int_{a}^{x+h} \ln ^{2} t d t-\int_{a}^{x} \ln ^{2} t d t}{h}\] equals to
- \(0\)
- \(\ln ^{2} x\)
- \(\frac{2 \ln x}{x}\)
- does not exist
Answer
(B) ^ 2 x
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- If _ 0 ^ x^ 2 (1+ x)^ 2 d x=A then _ 0 ^ 2 x^ 2 ^ 2 (x / 2) (1+ x)^ 2 d x=
- The value of the integral _ - / 2 ^ / 2 (x^ 2 + +x -x ) x d x is
- The area of the region ( x, y ) : xy ≤ 8, 1 ≤ y ≤ x 2 is
- Consider the function f(x)= _ 0 ^ x [t] d t where x>0 and is the integral part of . Then
- Assertion : If 1 f(x) d x=2 log | f (x)|+c, then f(x)= x 2 Reason : When f (x) = x 2 , then 1 f(x) d x= 2 x d…
- Evaluate (x+2) d x (x^ 2 +3 x+3 ) x+1
- Let f be a positive function. Let I_ 1 = _ 1-k ^ k x f[x(1-x)] d x I_ 2 = _ 1-k ^ k f[x(1-x)] d x where 2 k –…
- ( x 3 + 3 x 2 + 3 x + 3 + ( x + 1) cos ( x + 1)) dx is equal to
More Integral Calculus questions · Browse all practice questions