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If I(n) = int((pi)/(6)) "cosec"^(n) x dx...

If `I_(n) = int_((pi)/(6)) "cosec"^(n) x dx`, show that `(n-1)I_(n) = 2^(n-2) sqrt(3)+(n-2)I_(n-2)`

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AAKASH SERIES-DEFINITE INTEGRALS-Exercise - 2.4 (Level-1)
  1. int(0)^(2pi) sin^(7) x cos^(5) x dx

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  2. int(0)^(2pi) sin^(11) x cos^(10)x dx

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  3. Find the values of the following integrals (i) int(-2 pi)^(2pi) cos^...

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  4. Find underset(-pi//2)overset(pi//2)int sin^(2)x cos^(4)x dx

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  5. Find the value of the integral underset(-pi//2)overset(pi//2)int si...

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  6. int(-(pi)/(2))^((pi)/(2)) sin^(3) theta cos^(3) theta d theta

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  7. int(-pi//2)^(pi//2) sin^(2) x cos^(2) x(sin x + cos x) dx=

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  8. int(0)^(2pi) x sin^(6) x cos^(5) x dx=

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  9. Evaluate the following integrals (ii) int(0)^(pi) x sin^(5) x cos^(...

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  10. Find underset(0)overset(pi)int xsin^(7)x cos^(6)x dx

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

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  12. Evaluate int(0)^((1)/(2)) (x^(7))/(sqrt(1-x^(4))) dx

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  13. Find underset(-a)overset(a)int x^(2) (a^(2)-x^(2))^(3//2)dx

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  14. Evaluate the integral underset(0)overset(4) int (16-x^(2))^(5//2) d...

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  15. Evaluate the integral underset(0)overset(1) int x^(5) (1-x)^(5//2)d...

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  16. Find the value of the integral underset(0)overset(a) int x(a^(2)-x^...

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  17. Find the value of the integral underset(0)overset(2)int x^(3//2)sqr...

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  18. Evaluate int(0)^(1)x^(6) sin^(-1) x dx

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  19. If I(n) = int((pi)/(4))^((pi)/(2)) cot^(n) x dx, prove that I(n) + I(n...

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  20. If I(n) = int((pi)/(6)) "cosec"^(n) x dx, show that (n-1)I(n) = 2^(n-2...

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