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Ifint(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"th...

`Ifint_(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equal to"`
(a)4 (b) 1n 8 (c) 1n 4 (d) none of these

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The correct Answer is:
(i) Area bounded by `y = cos x`, x-axis between `x = 0, x = pi`.
(ii) Difference of area bounded by `y = cosx`, x-axis between `x = 0, x = pi/2` and area bounded by `y = cosx`, x -axis between `x = (pi)/(2), x = (3pi)/(2)`.
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
  1. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

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  2. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

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  3. If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then int(0)^(1...

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  4. int(0)^(pi)|1+2cosx| dx is equal to :

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  5. The value of int(1)^(3) (|x-2|+[x])dx is ([x] stands for greatest inte...

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  6. The value of int(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greate...

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  7. int(lnpi-ln2)^(lnpi) (e^(x))/(1-cos(2/3e^(x))) dx is equal to

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  8. If I(1)=int(e)^(e^(2))(dx)/(lnx) and I(2) = int(1)^(2)(e^(x))/(x) dx(1...

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  9. int(0)^(pi/4)(x.sinx)/(cos^(3)x) dx equal to :

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  10. The value if definite integral int(3/2)^(9/4)[sqrt(2x-sqrt(5(4x-5)))+s...

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  11. Ifint(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equal to" (a)4 ...

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  12. int(0)^(oo)(x^(2)+1)/(x^(4)+7x^(2)+1)dx=

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  13. Suppose for every integer n, .int(n)^(n+1) f(x)dx = n^(2). The value o...

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  14. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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  15. int- 1^1cot^(- 1)((x+x^3)/(1+x^4))dx

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

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

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

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

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

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