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If f and g are continuous [0,a) satisfyi...

If f and g are continuous [0,a) satisfying f(x) = f(a-x) and g(x)+ g(a-x) = 2 then, `int_0^(a) f(x) g(x) dx =`

A

`int_0^(a) g(x) dx`

B

`int_0^(a) f(x) dx`

C

0

D

none of these

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The correct Answer is:
B
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  2. int0^(pi/2) (dx)/(1+cotx) =

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  3. If f and g are continuous [0,a) satisfying f(x) = f(a-x) and g(x)+ g(a...

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  4. int0^(3) |x^(3)+x^(2)+3x| dx is equal to

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  5. int0^(10) |x(x-1)(x-2)| dx is equal to

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  6. If I = int0^(pi/4) log (1+ tan x) dx, then I =

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  7. lim(n rarr oo) {1/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

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  8. If I = int(-pi)^(pi) (e^(sinx))/(e^(sinx)-e^(-sinx)) dx then I =

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  9. lim(x rarr oo) (int(0)^(2x) xe^(2)dx)/(e^(4x^(2))) equals :

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  10. The value of int(-2)^(2) { p log ((1+x)/(1-x))+ q log ((1-x)/(1+x))^(...

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  11. inta^(b) |x|/x dx, (Where 0 lt a lt b) =

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  12. The area of the region bounded by the curve y^(2)=8x and the line y=2x...

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  13. The area bounded by y = 4x-x^(2) and x-axis is

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  14. int(1)^(3)(x-1)(x-2)(x-3)dx=

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  15. The area bounded by x-axis and the curve y=4x-x^(2)-3 is

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  16. Area bounded by y = log x, the x-axis and the line x=2 is

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  17. The area enclosed between the parabolas y^(2) = 4x and x^(2)=4y is

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  18. The area bounded by the curve y = log x, the x-axis and the line x=e i...

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  19. The area enclosed between the curves y = x^(3) and y=sqrtx is, (in squ...

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  20. The area enclosed between the parabola y=x^(2)-x+2 and the line y=x+2 ...

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