Home
Class 12
MATHS
Let g(t) = underset(x(1))overset(x(2))in...

Let `g(t) = underset(x_(1))overset(x_(2))intf(t,x) dx`. Then `g'(t) = underset(x_(1))overset(x_(2))int(del)/(delt) (f(t,x))dx`, Consider `f(x) = underset(0)overset(pi)int (ln(1+xcostheta))/(costheta) d theta`.
The number of critical point of `f(x)`, in the interior of its domain, is

A

discontinuous at `x = 0`

B

differentiable at `x = 1`

C

continuous at `x = 0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - I|49 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - III|25 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

Let g(t) = int_(x_(1))^(x^(2))f(t,x) dx . Then g'(t) = int_(x_(1))^(x^(2))(del)/(delt) (f(t,x))dx , Consider f(x) = int_(0)^(pi) (ln(1+xcostheta))/(costheta) d theta . The number of critical point of f(x) , in the interior of its domain, is

The integral underset(1)overset(5)int x^(2)dx is equal to

The value of the integral underset(e^(-1))overset(e^(2))int |(log_(e)x)/(x)|dx is

The value of integral underset(2)overset(4)int(dx)/(x) is :-

If I=underset (0)overset(1) int cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

If overset(4)underset(-1)int f(x)=4 and overset(4)underset(2)int (3-f(x))dx=7 , then the value of overset(-1)underset(2)int f(x)dx , is

overset(pi//2)underset(-pi//2)int (cos x)/(1+e^(x))dx=

Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2) . The value of underset(-2)overset(4)intf(x)dx is :

If I=overset(1)underset(0)int (1)/(1+x^(pi//2))dx then

The points of extremum of underset(0)overset(x^(2))int (t^(2)-5t+4)/(2+e^(t))dt are