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If f(a+b - x) = f(x) , then int(a)^(b)...

If ` f(a+b - x) = f(x) ,` then ` int_(a)^(b) x f(x) dx` is equal to

A

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

B

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

C

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

D

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

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The correct Answer is:
A, C
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. The value of int (0) ^([x]){x} dx is

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  2. If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) an...

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  3. If f(a+b - x) = f(x) , then int(a)^(b) x f(x) dx is equal to

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  4. If int(0)^(pi) x f (sin x) dx = A int (0)^(pi//2) f(sin x) dx , then A...

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  5. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

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  6. The value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x)dx where agt 0, is

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  7. overset(pi//2)underset(-pi//2)int (|x|)/(8 cos^(2)2x+1)dxhas the value

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  8. int(0)^(pi//2)(1)/(1+tan^(3)x)dx=

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  9. int (-1) ^(1) (x ^(4))/( 1 + e ^(x ^(7)))dx is

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  10. int (-1) ^(1) (sin x + x ^(2))/( 3 - |x|) dx

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  11. The value of overset(pi//4)underset(-pi//4)int(e^(x)sec^(2)x)/(e^(2x)-...

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  12. int ( -pi) ^(pi) (2x ( 1+ sin x ))/(1+ cos ^(2) x )

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  13. int (0) ^(pi) (cos ^(2) x ) dx,

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  14. If int0^11 (11^x)/(11^([x])) dx=k/(log 11) then value of k is (where [...

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  15. Let Tgt0 be a fixed real number. Suppose f is a cintinuous function s...

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  16. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

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  17. The value of lim(xto0) (int(0)^(x^2)sec^2t dt)/(x sin x) dx , is

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  18. underset( x to 0) lim ( int(0)^(x^(2)) cos^(2)t" "dt)/(x sin x) = ...

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  19. If int0^y cos t^2\ dt = int0^(x^2)\ sint/t \ dt, then dy/dx is equal t...

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  20. let f(x)=int(t^2-t+1)dt,AA x in (3,4), then the difference between th...

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