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Compute the integrals : (a) int(0)^(...

Compute the integrals :
(a) `int_(0)^(pi//2) (cos x dx)/( 6 - 5 sin x + sin^(2) x)`
(b) `int _(0)^(pi//2) (dx)/( 2 + cos x)`

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Verified by Experts

The correct Answer is:
(a) In `(4)/(3)`
(b) `(pi)/( 3 sqrt(3))`
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IA MARON-THE DEFINITE INTEGRAL -6 . 4 (Changing the Variable in a Definite Integral)
  1. The value of the integral overset(4)underset(2)int (sqrt(x^(2)-4))/(x^...

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  2. Compute the integrals : (a) int(0)^(0) x^(2) sqrt(a^(2) - x^(2)) dx...

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  3. Compute the integrals : (a) int(0)^(pi//2) (cos x dx)/( 6 - 5 sin ...

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  4. Compute the integral int(0)^(pi//4) (dx)/( a^(2) cos^(2) x + b^(2) ...

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  5. Compute the integrals (a) int(1)^(sqrt(3)) (sqrt(1 + x^(2)))/(x^(2)...

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  6. The value of the integralunderset(0)overset(pi)int (x sin x)/(1+cos^(2...

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  7. Evaluate the integral I = int(0)^(1) (I n (1 + x))/( 1 + x) dx

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  8. Prove that for any given integral with finite limits a and b one can...

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  9. Evaluate int(-4)^(-5)e^((x+5^(2))) dx+3int(1//3)^(2//3)e^(9(x-(2)/(3))...

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  10. Prove that the integral int(0)^(pi) (sin 2 k x)/(sin x) dx equal...

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  11. Compute the integral int(1//2)^(sqrt(3//2)) (dx)/(x sqrt(1 - x^(2)))

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  12. Prove that the function L(x) defined on the interval (0,infty) by the ...

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  13. Transform the integral int(0)^(3) (x-2)^(2) dx by the substitution (x...

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  14. Compute the integrals I = int(0)^(1)(dx)/(1 + sqrt(x))

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  15. Compute the integrals I = int(0)^(5) (dx)/( 2 x + sqrt(3 x + 1))

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  16. Compute the integrals I = int(pi//4)^(pi//3) (dx)/( 1 - sin x)

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  17. Compute the integrals I = int(0)^(1) sqrt(2 x - x^(2)) dx

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  18. Compute the integrals I = int(0)^(pi//4) (sin x + cos x)/( 3 + si...

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  19. Compute the integrals I = int(0)^(a) x^(2) sqrt((a - x)/( a + x))...

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  20. Compute the integrals I = int(0)^(2a) sqrt(2 a x - x^(2)) dx

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