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If f is an integrable function, show tha...

If `f` is an integrable function, show that `int_(-a)^af(x^2)dx=2int_0^af(x^2)dx`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. If f is an integrable function such that f(2a-x)=f(x), then prove that...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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