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Evaluate the following definite integral...

Evaluate the following definite integral: `int_0^(pi//4)s e c\ x\ dx`

Text Solution

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`\int_{0}^{\frac{\pi}{4}} \sec x d x `
`=[\log (\sec x-\tan x)]_{0}^{\frac{\pi}{4}} `
`=[\log (\sec \frac{\pi}{4}-\tan \frac{\pi}{4})-\log (\sec 0-\tan 0)] `
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following definite integral: int0^(pi//2)(sinx+cos x)dx

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  2. Evaluate the following definite integral: int(pi//4)^(pi//2)cotx\ dx

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  3. Evaluate the following definite integral: int0^(pi//4)s e c\ x\ dx

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  4. Evaluate the following definite integral: int(pi//6)^(pi//4)cos e c\ x...

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  5. Evaluate : int0^pi1/(1+sinx)dx

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  6. Evaluate the definite integrals int0^(pi/2)cos^2x""""dx

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  7. Evaluate the following definite integral: int0^(pi//6)cosxcos2x\ dx

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  8. Evaluate : int(pi/3)^(pi/4)(tanx+cotx)^2dx

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  9. Evaluate the following definite integral int0^(pi/2) cos^4 x dx

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  10. Evaluate the following definite integral: int0^(pi//2)(a^2 cos^2x+b^2s...

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  11. Evaluate the following definite integral: int0^(pi//2)sqrt(1+cosx\ )dx

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  12. Evaluate the following definite integral: int0^1(1-x)/(1+x)dx

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  13. Evaluate the following definite integral: int(-pi//4)^(pi//4)1/(1+s in...

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  14. Evaluate the following definite integral: int0^(pi//2)cos^3x\ dx

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  15. Evaluate the following definite integral int0^(pi/2) cos^4 x dx

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  16. Evaluate the following definite integral: int0^(pi//2)x^2sinx\ dx

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  17. Evaluate the following definite integral: int0^(pi//2)cosx\ dx

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  18. Evaluate the following definite integral: int0^(pi//2)x^2sin x\ dx

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  19. Evaluate the following definite integral: int0^(pi//2)cos^2x\ dx

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  20. Evaluate the following definite integral: int1^3(logx)dx

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