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Evaluate : int(0)^(pi) (x sin x )/(1 + ...

Evaluate : `int_(0)^(pi) (x sin x )/(1 + sin x ) dx `

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`pi(pi/2 - 1)`
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MAHAVEER PUBLICATION-DEFINITE INTEGRAL-QUESTION BANK
  1. int1^2 x/((x+1)(x+2))dx

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  2. Find the Definite Integrals : int1^2 e^x((x-1)/x^2) dx

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  3. int0^1 sqrt((1-x)/(1+x)) dx

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  4. Find the Definite Integrals : int0^1 x^2e^(x^3) dx

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  5. Evaluate the following integral: int0^1(tan^(-1)x)/(1+x^2)dx

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  6. int0^(pi/2) sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))dx

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  7. Using the properties of definite integral Evaluate : int0^(pi/2) sinx ...

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  8. Using the properties of definite integral Evaluate : int(pi/6)^(pi/3) ...

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  9. Using the properties of definite integral Evaluate : int0^(pi) x /(1 +...

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  10. By using the properties of definite integrals, evaluate the integra...

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  11. Using the properties of definite integral Evaluate : int0^3 x sqrt(3-x...

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  12. By using the properties of definite integrals, evaluate the integra...

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  13. By using the properties of definite integrals, evaluate the integra...

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  14. Evaluate int0^(pi/2) (sinx-cosx)/(1+sinxcosx)dx

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  15. Using the properties of definite integral Evaluate : int0^(pi) (xtanx)...

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  16. Evaluate : int(0)^(pi) (x sin x )/(1 + sin x ) dx

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  17. Evaluate lim(nrarroo) [1/n + 1/(n+1) + 1/(n+2) +…+ 1/(3n)]

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  18. lim(n rarr oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))

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  19. underset(nrarroo)lim[(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+....

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  20. Evaluate lim(nrarroo) n [1^2/(n^3+1^3) + 2^2/(n^3+2^3) + 3^2/(n^3+3^3)...

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