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The value of int (1)^(e) 10^(log(e)x) dx...

The value of `int _(1)^(e) 10^(log_(e)x)` dx is equal to

A

`10 log_(e) (10e)`

B

`(10e-1)/(log_(e)10e)`

C

`(10e)/(log_(e)10 e)`

D

`(10 e) log_(e) (10e)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int_(1)^(e)10^(log_(e)x)dx`
Again, let `l_(1)=int10^(log_(e)x)dx`
`rArr" "l_(1)=x.10^(log_(e)x)-intx.10^(log_(e)x).(log_(e)10)/(x)dx`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  2. The value of int(e^(-1))^(e) (dt)/(t(t+1)) is equal to

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  3. The value of int (1)^(e) 10^(log(e)x) dx is equal to

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  4. If int (2)^(e) (1/(logx)-1/(logx)^(2))dx = a + b/(log2) , then

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  5. int (0)^(oo) (dx)/((x+ sqrt(x^(2)+1))^(3)) is equal to

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  6. The value of the integral int (-pi//2)^(pi//2) sqrt(cos x - cos ^(3) ...

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  7. The value of I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(...

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  8. int (alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

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  9. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  10. The value overset(2)underset(-2)int {p" In"((1+x)/(1-x))+q" In "((1-...

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  11. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

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  12. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

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  13. int (0)^(2pi) sin^(6) x cos^(5) x dx is equal to

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  14. int (-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] dx is equalt to

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  15. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  16. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

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  17. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equ...

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  18. The value of the integral int (0)^(pi//2) sin ^(5) x dx is

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  19. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

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  20. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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