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If `f(x)` and `g(x)` are continuous functions satisfying `f(x) = f(a-x)` and `g(x) + g(a-x) = 2`, then what is `int_(0)^(a) f(x) g(x)dx` equal to ?

A

`int _(0) ^(a ) g (x) dx `

B

`int _(0) ^(a ) f (x) dx`

C

0

D

None of these

Text Solution

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The correct Answer is:
B
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. int (0) ^(2npi) (|sin x | - [|(sin x )/(2) | ]) dx is equal to (where ...

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  2. The value of int (0) ^([x]){x} dx is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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