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int (0) ^(1//2) dx/((1-2x^(2))sqrt(1-x^(...

`int _(0) ^(1//2) dx/((1-2x^(2))sqrt(1-x^(2)))=`

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Verified by Experts

The correct Answer is:
`1/2 ln (2+ sqrt3)`
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int_(0)^((pi)/(2))(dx)/((1-2x^(2))sqrt(1-x^(2)))=(1)/(2)log(2+sqrt(3))

int_(0)^((pi)/(2))(dx)/((1-2x^(2))sqrt(1-x^(2)))=(1)/(2)log(2+sqrt(3))

int_(0)^(1//2)(dx)/((1+x^(2))sqrt(1-x^(2))) is equal to

int(1)/(1-x^(2)) sqrt(1-x^(2))dx

Evaluate the following integral: int_0^(1//2)1/((1+x^2)sqrt(1-x^2))dx

" 0."int_(1/2)^(1)(dx)/(x^(2)sqrt(1-x^(2)))

Evaluate: int_(0)^(1)(2-x^(2))/((1+x)sqrt(1-x^(2)))dx

"int_(-1)^(1)(dx)/((2-x)sqrt(1-x^(2)))

int_(0)^(1/sqrt2)(dx)/(sqrt(1-x^(2)))

MOTION-DEFINITE INTEGRATION -ELEMENTRAY EXERCISE
  1. int (0) ^(pi//4)cos 2x sqrt(1- sin 2x )dx

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  2. int ( 0)^(2) ((x )/(3-x)) dx

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  3. int (0) ^(1//2) dx/((1-2x^(2))sqrt(1-x^(2)))=

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  4. int (1) ^(2) (dx )/(x (x ^(4) + 1))

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  5. int (0) ^(pi//2) sin phi cos phi sqrt((a^(2) sin ^(2) phi cos ^(2)))d ...

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  6. The value of the definite integral overset(3pi//4)underset(0)int(1+x)s...

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  7. Let f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot The...

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  8. int (0) ^(1) x tan ^(-1) x dx =

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  9. Suppose that f,f^prime and f prime prime are continuous on [0, ln 2] a...

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  10. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

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  11. int (a) ^(b) (dx)/( sqrt(1 + x ^(2))) where a = (e-e^(-1))/( 2 ) &b = ...

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  12. int (x^(x)(x^(2x)+1)("ln"x+1))/(x^(4x)+1)dx

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  13. int (0) ^(1) x ^(5) sqrt((1 + x ^(2))/(sqrt(1- x^(2))))dx

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  14. Suppose that the function f, g, f',and g' are continuous over [0,1], g...

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  15. The value of the integral overset(pi//4)underset(0)int (sin theta+cos ...

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  16. int (0) ^(pi) sin ^(2) theta cos theta d theta

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  17. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

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  18. int (0) ^(pi//2) (x + sin x )/(1 + cos x ) dx

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  19. Let A = int (3//4) ^(4//3) (2x ^(2) + x +1 )/( x ^(3) + x ^(2) + x + 1...

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  20. int (2 -x ^(2))/( ( a + 1) (1- x ^(2)))dx

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