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int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=...

`int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=`

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The correct Answer is:
`(b-a)/(2)`
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int_(0)^(a)(f(x))/(f(x)+f(a-x))dx=

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int _(a) ^(b) f (x) dx =

int_(0)^(a) (f(a+x) + f(a-x) ) dx =

Property 4: If f(x) is a comtinuous function on [a;b] then int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

int_(a)^( Prove that: )(f(x))/(f(x)+f(a+b-x))dx=(b-a)/(2)

If a lt b lt c in R and f (a + b +c - x) = f (x) for all, x then int_(a)^(b) (x(f(x) + f(x + c))dx)/(a + b) is:

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CBSE COMPLEMENTARY MATERIAL-INTEGRALS-SIX MARK QUESTIONS
  1. int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=

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  2. int(x^5+4)/(x^5-x)dx

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  3. int(2e^t)/(e^(3t)-6e^(2t)+11 e^t-6)dt

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  4. int(2x^3)/((x+1)(x-3)^2)dx

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  5. Evaluate the following integrals: int(1+sinx)/(sin x(1+cosx))dx

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  6. int(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))dx

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  7. Evaluate: int0^1xsqrt((1-x^2)/(1+x^2))dx

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  8. Evaluate the following integrals: int(0)^(pi//2) (cosx)/(1+cos x+sin...

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  9. Evaluate the following integrals as limit of sums: int(2)^(4)(2x+1)d...

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  10. Evaluate the following integrals as limit of sums: int(0)^(2)(x^(2)+...

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  11. Evaluate the following integrals as limit of sums: int(1)^(3)(3x^(2)...

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  12. Evaluate the following integrals as limit of sums: int(0)^(4)(3x^(2)...

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  13. Evaluate the following integrals as limit of sums: int(0)^(1)e^(2-3x...

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  14. Evaluate the following integrals as limit of sums: int(0)^(1)(3x^(2)...

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  15. Evaluate: int1/((sinx-2cosx)(2sinx+cosx)dx

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  16. int0^1log(1+x)/(1+x^2)dx

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  17. int(0)^(pi//2) (2logsin x - log sin 2x) dx=

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  18. Evaluate: int0^1x(tan^(-1)x)^2dx

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  19. Prove that: int(0)^(pi//2) log (sin x) dx =int(0)^(pi//2) log (cos x)...

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  20. Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dxdot Henc...

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  21. Evaluate : int0^(pi/2)(sin^2x)/(s in x+cos x)dx

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