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The value of int (pi//4) ^(pi//3) cosec ...

The value of `int _(pi//4) ^(pi//3) cosec x d (sin x ) ` for `0 lt x lt pi //2` is

A

`ln 2`

B

` 1/2 ln 3/2`

C

`ln ((sin 1//2)/( sin 1//sqrt2))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. int (0) ^(pi//4) sin (x- [x])d (x-[x]) is equal to

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  2. For 0 lt x lt pi/2, int (1//sqrt2) ^(1//2) cot x s (cos x ) equal to

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  3. The value of int (pi//4) ^(pi//3) cosec x d (sin x ) for 0 lt x lt pi...

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  4. Find the value of : int0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denote...

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  5. int (log pi - log 2 ) ^(log pi) (e ^(x))/(1- cos ((2)/(3)e ^(x)))dx i...

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  6. If underset(0)overset(oo)int e^(-x^(2))dx=sqrt((pi)/(2))"then"underset...

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  7. Let A = underset(0)overset(1)int(e^(t))/(1+t) dt, then underset(a-1)ov...

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  8. Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0, If int(1)^(4) (3)/(x) ...

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  9. 1/c int (a) ^(b) f ((x)/(c )) dx =

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  10. int(5/2)^5 (sqrt((25-x^2)^3))/(x^4) dx

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  11. If {:(f(x)=x", ...."x lt 1),(" "=x-1", ...." x ge 1","):} ...

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  12. Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2...

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  13. int (0) ^(pi) (1 + 2 cos x ) dx equal to :

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  14. The value of int (-1) ^(3) (|x-2 |+[x]) dx is equal to (where [**] den...

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  15. If underset(-1)overset(3//2)int|xsinpix|dx = (k)/(pi^(2)), then the va...

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  16. int0^(10pi) |sin x| dx is

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  17. The value of int (-1) ^(3) | 1- x ^(2) | dx is -

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  18. rArrunderset(0)overset(oo)int[(2)/(e^(x))]dx (where [*] denotes the gr...

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  19. int0^sqrt2 [x^2]dx

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  20. If f (x) = int (0) ^(x) sin [2x] dx then f ( pi//2) is (where [**] de...

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