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int3^(10)[log[x]]dxi se q u a lto(w h e ...

`int_3^(10)[log[x]]dxi se q u a lto(w h e r e[dot]r e p r e s e t n tt h egr e a t e s t` integer function) 9 (b) `16-e` (c) 10 (d) `10+e`

A

9

B

`16-e`

C

`10`

D

`10+e`

Text Solution

Verified by Experts

The correct Answer is:
A
When `ele[x]lt e^(2), 1le log [x]lt 2`
when `e^(2) le [x] lte^(3), 2lt log [x] lt 3`
`:.int_(3)^(8)1 dx+int_(8)^(10)2dx=9`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. If agt0 and A=int(0)^(a)cos^(-1)xdx, and int(-a)^(a)(cos^(-1)x-sin^(...

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  2. The value of int1^a[x]f^(prime)(x)dxf^(prime)(x)dx ,w h e r ea >1,a n ...

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  3. int3^(10)[log[x]]dxi se q u a lto(w h e r e[dot]r e p r e s e t n tt h...

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  4. int(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer...

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  5. T h ev a l u eofint(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes ...

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  6. Evaluate: int0^(2pi)[sinx]dx ,w h e r e[x] denotes the greatest integ...

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  7. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

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  8. G i v e nint0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integr...

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  9. "I f"I1=int(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I2=int(-10...

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  10. The value of int0^oo(x dx)/((1+x)(1+x^2)) is equal to

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  11. about to only mathematics

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  12. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)]dx , I2=i...

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  13. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I2=int(f...

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  14. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

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  15. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is sqrt(...

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  16. f(x)>0AAx in Ra n di sbou n d e ddotIf (lim)(nvecoo)[int0^a(f(x)dx)/...

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  17. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,t h e nlambdai s...

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  18. The value of the definite integral int0^1(1+e^-x^2)dx (b) 2 1+e^...

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  19. T h ev a l u eoft h ein t egr a lint(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(...

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  20. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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