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By using the properties of definite inte...

By using the properties of definite integrals, evaluate the integrals
Show that `int_(0)^(a)f(x)g(x)dx=2int_(0)^(a)f(x)dx`, if f and g are defined as `f(x)=f(a-x)` and `g(x)+g(a-x)=4`.

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The correct Answer is:
`2int_(0)^(2)f(x)dx`
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NEW JOYTHI PUBLICATION-INTEGRALS -EXERCISE 7.11
  1. By using the properties of definite integrals, evaluate the integrals ...

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  2. By using the properties of definite integrals, evaluate the integrals ...

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  3. By using the properties of definite integrals, evaluate the integrals ...

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  4. By using the properties of definite integrals, evaluate the integrals ...

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  5. int- 5^5|x+2|dx

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  6. evaluate the integrals int(2)^(8)|x-5|dx

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  7. evaluate the integrals int(0)^(1)x(1-x)dx

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  8. By using the properties of definite integrals, evaluate the integrals ...

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  9. evaluate the integrals intxsqrt(2-x)dx

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

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  11. By using the properties of definite integrals, evaluate the integrals ...

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

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

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  14. By using the properties of definite integrals, evaluate the integrals ...

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  15. By using the properties of definite integrals, evaluate the integrals ...

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  16. By using the properties of definite integrals, evaluate the integrals ...

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  17. evaluate the integrals int(0)^(4)|x-1|dx

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  18. By using the properties of definite integrals, evaluate the integrals ...

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  19. The value of int((-pi)/(2))^((pi)/(2))(x^(3)+xcosx+tan^(5)x+1)dx is

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  20. The value int(0)^((pi)/(2))log((4+3sinx)/(4+3cosx))dx is

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