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The range of the function f(x)=int(-1)^(...

The range of the function `f(x)=int_(-1)^(1)(sinxdt)/(1+2tcosx+t^(2))` is

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The correct Answer is:
`{- (pi)/(2), (pi)/(2)}`
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MOTION-DEFINITE INTEGRATION -EXERCISE -3
  1. Evaluate : int0^(2pi)e^xcos(pi/4+x/2)dx

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  2. Evaluate: int (0) ^(1) e ^(ln tan ^(-1)) x. sin ^(-1) (cos x ) dx.

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  3. The range of the function f(x)=int(-1)^(1)(sinxdt)/(1+2tcosx+t^(2)) is

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  4. Evaluate I (n) = int (1) ^(e) (ln ^(n) x) dx hence find I (3).

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  5. int0^sqrt3 sin^-1\ (2x)/(1+x^2)\ dx

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  6. For a >= 2, if the value of the definite int0^oo(dx)/(a^2+(x-(1/ x))^2...

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  7. The value of underset(0)overset(1)int({2x}-1)({3x}-1)dx, (where {} de...

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  8. Find the value of the definite integral int0^pi | sqrt (2)sin x+2 cos ...

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  9. Evaluate the integral int (3) ^(5) (sqrt(x +2 sqrt(2x-4))+ sqrt(x-2 ...

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  10. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

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  11. Evaluate : int- 1^1((2x^(332)+x^(998)+4x^(1668)*sinx^(691))/(1+x^(666)...

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  12. int (-1) ^(2) (x ^(2) -x)/(sqrt(x ^(2) + 4))

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  13. int (0) ^(pi//4) (xdx )/(cos x (cos x + sin x ))

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  14. Evaluate :int0^(pi/2)(asinx+bcosx)/(sin(pi/4+x))dx

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  15. int (0) ^(pi) ((ax +b) sec c tan x)/(4 + tan ^(2) x ) dx (a,b gt 0)

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  16. int0^pi((2x+3)sinx)/((1+cos^2x)dx

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  17. intxsin^(- 1)[1/2sqrt((2a-x)/a)]dx

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  18. f,g, h , are continuous in [0, a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-...

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  19. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

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  20. The value of the integral underset(0)overset(pi)int (xdx)/(1+cos alpha...

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