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Evaluate the following integral:int0^pix...

Evaluate the following integral:`int_0^pixlogsinx\ dx`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate the following integral:int0^pixsinxcos^4x\ dx

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  2. Evaluate the following integral:int0^pixlogsinx\ dx

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  3. Evaluate the following integral:int0^pixlogsinx\ dx

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  4. Evaluate the following integral: 'intpi//3^(pi//6) {1/(1+cot^(3/2)x)}...

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  5. Evaluate the following integral:int(pi//6)^(pi//3)1/(1+cot^(3//2)x)dx

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  6. Evaluate the following integral:int2^8(sqrt(10-x))/(sqrt(x)+sqrt(10-x)...

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  7. Evaluate the following integral:int0^(pi//2)(xsinxcosx)/(sin^4x+cos^4x...

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  8. Evaluate the following integral:int(-pi//2)^(pi//2)sin^2x\ dx

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  9. Evaluate the following integral:int(-pi//4)^(pi//4)sin^2x\ dx

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  10. Evaluate the following integral:int(-pi//2)^(pi//2)log((2-sinx)/(2+sin...

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  11. Evaluate the following integral:int(-3pi//2)^(-pi//2){sin^2(3pi+x)+(pi...

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

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  13. Evaluate the following integral:int0^(2pi)sin^(100)xcos^(101)x\ dx

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  14. If f is an integrable function such that f(2a-x)=f(x), then prove that...

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  15. If f(2a-x)=-f(x), prove that int0^(2a)f(x)dx=0

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  16. If f is an integrable function, show that int(-a)^af(x^2)dx=2int0^af(x...

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  17. If f is an integrable function, show that int(-a)^a xf(x^2)dx=0

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  18. If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove t...

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  19. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx =(a+b)/2inta^bf(x...

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  20. If f(a+b-x)=f(x) , then prove that inta^b xf(x)dx=((a+b)/2)inta^bf(x)...

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