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int(-1)^(1)xln(1+e^(x))dx=...

`int_(-1)^(1)xln(1+e^(x))dx=`

A

`0`

B

`ln(1+e)`

C

` ln(1+e)-1`

D

`1//3`

Text Solution

Verified by Experts

The correct Answer is:
D
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
  1. int- 1^1cot^(- 1)((x+x^3)/(1+x^4))dx

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  2. int(2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)} dx is equal to

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  3. int(-1)^(1)xln(1+e^(x))dx=

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  4. If int(-1)^(3//2)|xsinpix|dx = (k)/(pi^(2)), then the value of k is :

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  5. The value of definite integral int0^(pi^2/4) dx/(1+sin^2 sqrtx+ cos^2 ...

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  6. int(2-ln3)^(3+ln3)(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal to :

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  7. The value of the definite integral l = int(0)^(x)xsqrt(1+|cosx|) dx is...

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  8. The value of int(0)^(pi//2)ln|tanx+cotx| dx is equal to :

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  9. If I1=int0^1(e^x)/(1+x) dxaand I2=int0^1 x^2/(e^(x^3)(2-x^3)) dx then ...

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  10. The value of int(0)^(|x|){x} dx (where [*] and {*} denotes greatest in...

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  11. If int(0)^(11) (11^(x))/(11^([x]))dx = k/(log11), (where [] denotes gr...

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  12. f(x) = int(x)^(x^(2))(e^(t))/(t)dt, then f'(t) is equal to :

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  13. f(x) = underset(0)overset(x)(t-1)(t-2)^(2)(t-4)^(5) dt (xgt0) then num...

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  14. Lim(hto0)(int(a)^(x+h)ln^(2)tdt-inta^(x)ln^(2)tdt)/(h) equals to :

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  15. The value of the function f(x) = 1+x+int(1)^(x)(ln^(2)t+2lnt)dt, where...

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  16. If int(a)^(y)cost^(2)dt = int(a)^(x^(2))(sint)/(t) dt, then the value ...

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  17. If int(sinx)^(1)t^(2) (f(t)) dt = (1-sinx), then f ((1)/(sqrt(3))) is

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  18. The value of lim(a rarr oo)(1)/(a^(2))int(0)^(a)ln(1+e^(x))dx equals

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  19. f(x) = underset(1)overset(sinxcosy)int(y^(2)+y+1)dy, then

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  20. int(0)^(pi//2) sin^(4)xcos^(3)dx is equal to :

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