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int(1)^(4) log(e)[x]dx equals...

`int_(1)^(4) log_(e)[x]dx` equals

A

`log_(e)6`

B

`log_(e)3`

C

`log_(e)2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`I=underset(1)overset(4)int log_(e)[x]dx`
`rArr I= underset(1)overset(2)int log_(e)1dx+underset(2)overset(3)int log_(e) 2dx+underset(3)overset(4)int log_(e) 3dx`
`rArr I=log_(e) 2+log_(e)3= log_(e)6`
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. If rArr int(-1)^(-4) f(x)dx= 4 and int(2)^(-4) (3-f(x))dx=7 , then the...

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  2. For x in R and a continuous function f(x) , let I(1)int(sin^(2)t)^(1+c...

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  3. int(1)^(4) log(e)[x]dx equals

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  4. If [*] denots the greatest integer function then the value of the inte...

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  5. The value of int(0)^(100pi) sum(r=1)^(10) tan rx dx is equal to

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  6. If I(1)=int(0)^(pi//2) cos(sin x) dx,I(2)=int(0)^(pi//2) sin (cos x)...

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  7. For any n in N, the value of the intergral int(0)^(pi) (sin 2nx)/(sin...

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  8. For any n in N, int(0)^(pi) (sin^(2)nx)/(sin^(2)x)dx is equal to

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  9. For any n in N, int(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to

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  10. If I(n) int(-pi)^(pi) (sin nx)/((1+pi^(x))sinx)dx,n=0,1,2,... then whi...

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  11. If I(n)=int(0)^(pi//4) tan^(n)x dx, then (1)/(I(2)+I(4)),(1)/(I(3)+I...

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  12. Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x...

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  13. The vlaue of ((5050)int(0)^(1)(1-x^(50))^(100)dx)/(int(0)^(1) (1-x^(50...

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  14. If f and g are continuopus fucntions on [ 0, pi] satisfying f(x) +f(p...

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  15. If f(x) and g(x) are two continuous functions defined on [-a,a] then t...

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  16. Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f...

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  17. The value of the integral int(0)^(a//2) sin 2n x cot x dx, where n i...

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  18. The value of the integral rArr int(1)^(e^(6)) [ (log x)/(3)] dx , whe...

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  19. For any natural number n, theb value of rArr int(0)^(n^(2))[ sqrt(x)]d...

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  20. The value of the integral int(a)^(a+pi//2) (|sin x|+|cosx|)dx is

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