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Evaluate: (i) int1/(1+cos2x)\ dx (ii) ...

Evaluate:
(i) `int1/(1+cos2x)\ dx`
(ii) `int1/(1-cos2x)\ dx`

Text Solution

Verified by Experts

(i) `int1/(1+cos2x)\ dx`

`=(1/2)int(1)/(cos^2x)\dx`

`=(1/2)int sec^2x\dx`

`=(tanx)/(2) +C`


(ii) `int1/(1-cos2x)\ dx`

`=(1/2)int(1)/(sin^2x)\dx`

`=(1/2)int(cosex^2x)\dx`

...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: (i) int1/(1-cosx)\ dx (ii) int1/(1-sinx)\ dx

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  2. Evaluate: (i) int(tanx)/(secx+tanx)\ dx (ii) int(cos e c\ x)/(cos e c\...

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  3. Evaluate: (i) int1/(1+cos2x)\ dx (ii) int1/(1-cos2x)\ dx

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  4. Evaluate: (i) inttan^(-1)((sin2x)/(1+cos2x))\ dx (ii) intcos^(-1)(si...

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  5. Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2...

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  6. Evaluate: (i) int((x^3+8)(x-1))/(x^2-2x+4)\ dx (ii) int(atanx+bcotx)...

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  7. Evaluate: (i) int(x^3-3x^2+5x-7+x^2\ a^x)/(2x^2)\ dx (ii) int(cosx)...

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  8. Evaluate: (i) int(1-cosx)/(1+cosx)\ dx (ii) int{3sinx-4cosx+5/(cos^...

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  9. If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

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  10. If f^(prime)(x)=x+b ,\ \ f(1)=5,\ \ f(2)=13 , find f(x) .

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  11. If f^(prime)(x)=8\ x^3-2x ,\ \ f(2)=8, find f(x) .

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  12. If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=...

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  13. Write the primitive or anti-derivative of f(x)=sqrt(x)+1/(sqrt(x)) ...

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  14. Evaluate: int{(2x-3)^5+1/((7x-5)^3)+1/(sqrt(5x-4))+1/(2-3x)+sqrt(3x+2)...

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  15. Evaluate: (i) inte^(2x-3)\ dx (ii) inta^(3x+2)\ dx

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  16. Evaluate: (i) intsec^2(7-4x)\ dx (ii) int1/(sin^2xcos^2x)\ dx

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  17. Evaluate: (i) intcos e c^2(3x+2)\ dx (ii) intsin(a x+b)cos(a x+b)\ ...

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  18. Evaluate: (i) int(sin4x)/(sin2x)\ dx (ii) int(sin4x)/(cos2x)\ dx

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  19. Evaluate: int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)\ dx

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  20. Evaluate: intsqrt(1+sinx)\ dx ,0< x <pi//2.

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