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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 BANGLISH-INTEGRALS-EXERCISE 7.12
  1. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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

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  3. Evaluate the definite integrals int(0)^(pi/2)(2sinx+3)dx

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

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

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  6. Evaluate the definite integrals int(0)^(pi/4)e^(3x)sinxdx

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  7. Evaluate the definite integrals int(0)^(pi/2)sin2xdx

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  8. Evaluate the definite integrals int(0)^(3)e^xdx

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

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  10. Prove the following int(1)^(3)(dx)/(x^(2)(x+1))=2/3+log2/3

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

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

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  13. Prove the following int(0)^(pi/2)sin^(3)xdx=2/3

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

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  15. Prove the following int(0)^(1)sin^(-1)xdx=pi/2-1

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  16. Evaluate int(0)^(1)e^(2-3x)dx .

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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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