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Evaluate the following : int(0)^(pi//6...

Evaluate the following :
`int_(0)^(pi//6)(dx)/(3-2 sin^(2)x)`

Text Solution

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`(1)/(sqrt3)tan^(-1)((1)/(3))`
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Evaluate the following : int_(0)^(pi)x sin^(3)x dx

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-DEFINITE INTEGRALS-Examples for Practice
  1. int0^(pi/4) tan^4xdx=

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  2. Evaluate the following : int(0)^(pi//4)sec^(4)xdx.

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  3. Evaluate the following : int(0)^(pi//6)(dx)/(3-2 sin^(2)x)

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  4. Evaluate the following : int(0)^(pi//4)(dx)/(3+4 cos^(2)x)dx

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  5. Evaluate the following : int(0)^(pi//4)(dx)/(3 cos 2x+5)

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  6. Evaluate the following : int(0)^(pi//2)(1)/(5+4 cos x)dx

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  7. Evaluate the following : int(0)^(pi//2)(dx)/(3+5sinx).

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  8. Evaluate the following : int(0)^(pi//2)x^(2)sinxdx

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  9. Evaluate the following : int(0)^(1)tan^(-1)((2x)/(1-x^(2)))dx

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  10. Evaluate the following : int(0)^(1)x tan^(-1)xdx

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  11. Evaluate the following : int(0)^(1)e^(x^(2)).x^(3)dx

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  12. Evaluate the following : int(0)^(1)(cos^(-1)x)^(2)dx

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  13. Evaluate the following : int(0)^(11//sqrt2)(sin^(-1)x)/((1-x^(2))^(3...

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  14. Evaluate the following : int(1)^(2)(x+3)/((x(x+2))dx

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  15. Evaluate the following : int(0)^(pi//4)(sec^(2)x)/((1+tanx)(2+tanx))...

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  16. Evaluate the following : int(0)^(pi//2)(sinx cos x)/((2sinx+1)(sin x...

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  17. Evaluate the following : int(0)^(pi//4)e^(x)(1+tanx+tan^(2)x)dx

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  18. Evaluate the following definite integral: int1^2e^(2x)(1/x-1/(2x^2))dx

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  19. int(0)^(e^(2)){(1)/((logx))-(1)/((logx)^(2))}dx

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  20. Evaluate the following : int(1)^(pi//2)[sin (logx)+cos(logx)]dx.

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