Home
Class 12
MATHS
Iff(x)=int0^x2|t|dt ,t h e n g(x)=x|x|...

`Iff(x)=int_0^x2|t|dt ,t h e n` `g(x)=x|x|` `g(x)` is monotonic `g(x)` is differentiable at `x=0` `g^(prime)(x)` is differentiable at `x=0`

A

`g(x)=x|x|`

B

g(x) is monotonic

C

g(x) is differentiable at x = 0

D

g'(x) is differentiable at x = 0

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|113 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If g(x)=int_(0)^(x)2|t|dt, then (a)g(x)=x|x|(b)g(x) is monotonic (c) g(x) is differentiable at x=0(d)g'(x) is differentiable at x=0

Let f(x)=|x| and g(x)=|x^(3)|, then f(x) and g(x) both are continuous at x=0 (b) f(x) and g(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0

If g(x)=int_(0)^(x)cos^(4)t dt , then prove that g(x+pi)=g(x)+g(pi) .

If g(x)=int_(0)^(x)cos^(4)t dt, then g(x+pi) equals

For x in R ,f(x)=|log2-sinx| and g(x)=f(f(x)) , then (1) g is not differentiable at x=0 (2) g'(0)=cos(log2) (3) g'(0)=-cos(log2) (4) g is differentiable at x=0 and g'(0)=-sin(log2)

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

CENGAGE-DEFINITE INTEGRATION -Exercise (Multiple)
  1. Let f(x)=int(1)^(x)(3^(t))/(1+t^(2))dt, where xgt0, Then

    Text Solution

    |

  2. If inta^b|sinx|dx=8 and int0^(a+b)|cosx| dx=9 , then find the val...

    Text Solution

    |

  3. Iff(x)=int0^x2|t|dt ,t h e n g(x)=x|x| g(x) is monotonic g(x) is di...

    Text Solution

    |

  4. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

    Text Solution

    |

  5. T h ev a l u eofint0^oo(dx)/(1+x^4)i s s a m ea st h a tofint0^oo(x^...

    Text Solution

    |

  6. The value of int0^1e^x^(2-x)dx is <1 (b) >1 (c) > e^(-1/4) (d) <e^(...

    Text Solution

    |

  7. If int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=10, then

    Text Solution

    |

  8. The values of a for which the integral int0^2|x-a|dxgeq1 is satisfied ...

    Text Solution

    |

  9. If f(x)=int(0)^(x)|t-1|dt, where 0lexle2, then

    Text Solution

    |

  10. If f(2-x)=f(2+x) and f(4x)=f(4+x) for all x and f(x) is a function for...

    Text Solution

    |

  11. Off(x)=int0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s f(x)+f(pi)...

    Text Solution

    |

  12. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then

    Text Solution

    |

  13. IfIn=int0^1(dx)/((1+x^2)^n),w h e r en in N , which of the following...

    Text Solution

    |

  14. L e tf:[1,oo)vecRa n df(x)=int1^x(e^t)/t dt-e^xdotT h e n f(x) is an ...

    Text Solution

    |

  15. Iff(x)=inta^x[f(x)]^(-1)dxa n dinta^1[f(x)]^(-1)dx=sqrt(2),t h e n f(...

    Text Solution

    |

  16. A continuous function f(x) satisfies the relation f(x)=e^x+int0^1 e^xf...

    Text Solution

    |

  17. int0^x{int0^uf(t)dx}d ui se q u a lto int0^x(x-u)f(u)d u int0^x uf(...

    Text Solution

    |

  18. Which of the following statement(s) is/are TRUE?

    Text Solution

    |

  19. If int(0)^(x)[x]dx=int(0)^(|x|)x dx, (where [.] and {.} denotes the g...

    Text Solution

    |

  20. Consider the function f(theta)=int(0)^(1)(|sqrt(1-x^(2))-sintheta|)/(s...

    Text Solution

    |