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Choose the correct answers If f (a + b...

Choose the correct answers
If f (a + b - x) = f (x), then `int_(a)^(b)xf(x)` dx is equal to

A

`(a+b)/2int_(a)^(b)f(b-x)dx`

B

`(a+b)/2int_(a)^(b)f(b+x)dx`

C

`(b-a)/2int_(a)^(b)f(x)dx`

D

`(a+b)/2int_(a)^(b)f(x)dx`

Text Solution

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The correct Answer is:
D
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NCERT GUJARATI-INTEGRALS-EXERCISE 7.12
  1. Integrate the functions (x^(2)+x+1)/((x+1)^(2)(x+2))

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  2. Integrate the functions tan^(-1)sqrt((1-x)/(1+x))

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  3. Integrate the functions (sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))

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  4. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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  5. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

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  6. Evaluate the definite integrals int(0)^(pi/2)(cos^(2)xdx)/(cos^(2)x+...

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  7. Evaluate the definite integrals int(pi/6)^(pi/3)(sinx+cosx)/(sqrt(si...

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  8. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

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  9. Evaluate the definite integrals int(0)^(pi/4)(sinx+cosx)/(9+16sin2x)...

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  10. Evaluate the definite integrals int(0)^(pi/2)sin2xtan^(-1)(sinx)dx

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  11. Evaluate the definite integrals int(0)^(pi)(xtanx)/(secx+tanx)dx

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  12. Evaluate the definite integrals int(1)^(4)[abs(x-1)+abs(x-2)+abs(x-3...

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  13. Prove the following int(0)^(1)xe^(x)dx=1

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  14. Prove the following int(-1)^(1)x^(17)cos^(4)xdx=0

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  15. Prove the following int(0)^(pi/4)2tan^(3)xdx=1-log2

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  16. Evaluate int(0)^(1)e^(2-3x)dx as a limit of a sum.

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  17. Choose the correct answers int(dx)/(e^(x)+e^(-x)) is equal to

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  18. Choose the correct answers int(cos2x)/((sinx+cosx)^(2))dx is equal t...

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  19. Choose the correct answers If f (a + b - x) = f (x), then int(a)^(b)...

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  20. Choose the correct answers The value of int(0)^(1)tan^(-1)((2x-1)/(1...

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