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If f(a+b-x)=f(x) , then prove that inta...

If `f(a+b-x)=f(x)` , then prove that `int_a^b xf(x)dx=((a+b)/2)int_a^bf(x)dxdot`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove t...

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

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  3. 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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  4. Property 8: If f(x) is a continuous function defined on [-a; a] then i...

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  5. If int0^pi x f(sinx) dx=A int0^(pi/2) f(sinx)dx, then A is (A) pi/2 ...

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  6. Evaluate the following integrals as limit of sum: int0^2(x+4)dx

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  7. Evaluate: int(2x+1)dx

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  8. Evaluate the following integrals as limit of sum: int0^3(x+4)dx

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  9. Evaluate the following integrals as limit of sum: int1^3(3x-2)dx

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  10. Evaluate the following integrals as limit of sum: int1^3(3x-2)dx

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  11. Evaluate int(x+1)""dx

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  12. Evaluate: int3^5(2-x)dx

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  13. Evaluate the definite integrals as limit of sums intz^1x^2dx

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  14. Evaluate the following integrals as limit of sum: int1^2(x^2-1)dx

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  15. Evaluate the following integrals : int0^2(x+3)dx

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  16. Evaluate the following integrals : int(-1)^1(x+3)dx

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  17. Evaluate the following integrals as limit of sum: int1^3(2x+3)dx

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  18. Evaluate the following integrals int1^3(2x+3)dx

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  19. Evaluate the following integrals as limit of sum: int0^2(x^2+1)dx

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  20. Evaluate the following integrals : int2^3(2x^2+1)dx

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