Home
Class 12
MATHS
If g(x)=int(0)^(x)cos^(4)t dt, then g(x+...

If `g(x)=int_(0)^(x)cos^(4)t dt,` then `g(x+pi)` equals to (a)`(g(x))/(g(pi))` (b)`g(x)+g(pi)` (c)`g(x)-g(pi)` (d)`g(x).g(pi)`

A

`g(x)+g(pi)`

B

`g(x)-g(pi)`

C

`g(x) g(pi)`

D

`g(x)//g(pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`g(x)=underset(0)overset(x)intcos^(4)`
`:. g(x+pi)=underset(0)overset(x +pi)intc os^(4)t dtunderset(0)overset(pi)int cos^(4)t dt+underset(pi)overset(x+pi)intcos^(4) t dt`
`rArr :. g(x+pi)=g(pi)+underset(0)overset(x +pi)intcos^(4)(u +pi)`, where `t=u+pi`
`rArr g(x+pi)=g(pi)+g(x)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|143 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If g(x)=int_0^xcos^4tdt , then g(x+pi) equals (a) g(x)+g(pi) (b) g(x)-g(pi) (c) g(x)g(pi) (d) (g(x))/(g(pi))

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

If g(x)""=int0xcos4t"dt" , then g(x""+pi) equals: (1) g(x)/(g(pi) (2) g(x)+g(pi) (3) g(x)-g(pi) (4) g(x)dotg(pi)

If g(x)=int_0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where n in N , (a) g(x)+g(pi) (b) g(x)+g((npi)/(2)) (c) g(x)+g(pi/2) (d) none of these

If g(x)=int_0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, where n in N , a) g(x)+g(pi) (b) g(x)+ng((pi)/(n2)) c) g(x)+g(pi/2) (d) none of these

If f(x) = 2 sinx, g(x) = cos^(2) x , then the value of (f+g)((pi)/(3))

If g(x)=int_(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(pi/2)=-2pi (b) g^(prime)(-pi/2)=-2pi (c) g^(prime)(-pi/2)=2pi (d) g^(prime)(pi/2)=2pi

If (x-1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of (a) f(x)g(x) (b) -f\ (x)+\ g(x) (c) f(x)-g(x) (d) {f(x)+g(x)}g(x)

If differentiable function f(x) in inverse of g(x) then f^(g(x)) is equal to (g^(x))/((g^(prime)(x))^3) 2. 0 3. (g^(x))/((g^(prime)(x))^2) 4. 1

If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to (A) f(a) = g(c ) (B) f(b) = g(b) (C) f(d) = g(b) (D) f(c ) = g(a)

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. If int(0) ^(x) f (t) dt = x + int (x ) ^(1) t f (t) dt, then the v...

    Text Solution

    |

  2. Let f be a positive function. Let I(1)=int(1-k)^(k)x f[x(1-x)]dx , I(...

    Text Solution

    |

  3. If g(x)=int(0)^(x)cos^(4)t dt, then g(x+pi) equals to (a)(g(x))/(g(pi)...

    Text Solution

    |

  4. If l(n)=int(0)^(pi//4) tan^(n)x dx, n in N "then" I(n+2)+I(n) equals

    Text Solution

    |

  5. If rArr I(n)=int(0)^(pi//4) tan ^(n)x dx, then for any positive integ...

    Text Solution

    |

  6. Find the value of int(-1)^1d/(dx)(tan^(-1)(1/x))dx

    Text Solution

    |

  7. The value of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

    Text Solution

    |

  8. If =int(1)^(e) (logx)^(n) dx, "then"I(n)+nI(n-1) is equal to

    Text Solution

    |

  9. If =int(0)^(1) x^(n)e^(-x)dx "for" n in N "then" I(n)-nI(n-1)=

    Text Solution

    |

  10. The value of int(1//n)^((an-1)//n) (sqrt(x))/(sqrt(a-x)+sqrtx)dx, is

    Text Solution

    |

  11. The value of the integral int(0)^(pi//2)log |tan x cot x |dx is

    Text Solution

    |

  12. If I(1)=int(x)^(1)(1)/(1+t^(2)) dt and I(2)=int(1)^(1//x)(1)/(1+t^(2))...

    Text Solution

    |

  13. The value of int(1/e->tanx) (tdt)/(1+t^2) + int(1/e->cotx) (dt)/(t*(1+...

    Text Solution

    |

  14. The absolute value of int(10)^(19) (cosx)/(1+x^(8))dx, is

    Text Solution

    |

  15. If f(x) is an odd pefiodc function defined on the interval [T/2,T/2], ...

    Text Solution

    |

  16. If int(pi//2)^(theta) sin x dx=sin 2 theta then the of theta satisfyin...

    Text Solution

    |

  17. If f(x) is periodic function with period, T, then

    Text Solution

    |

  18. The value of lim(n rarr infty) (1)/(n) {(n+1)(n+2)(n+3)…(n+n)}^(1//n)...

    Text Solution

    |

  19. The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...

    Text Solution

    |

  20. int(-2)^(2) min(x-[x],-x-[x])dx equals, where [x] represents greates i...

    Text Solution

    |