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True or False: underseta oversetb int f(...

True or False:
`underseta oversetb int f(x)dx ne underseta oversetb int f(a+b-x)dx`

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Prove that underset0oversetaint f(x)dx=underset0overseta int f(a-x)dx .

True or False: underset0 overset(pi)int cos^5 x dx ne 0

True or False: underset0oversetpi int cos^2xdx ne 2underset0overset(pi/2) int sin^2x dx

True or False: underset0overset(pi/2)int log|sinx|dx ne underset0overset(pi/2)int log(cosx)dx .

underset(a+b)overset(b+c)int f(x)dx is equal to

If underseta oversetb int x^3 dx=0 and underseta oversetb int x^2dx=2/3 , find the value of a and b.

True or False: underseta oversetb int f(x)dx , if it exists, is a uniquely determined real number.

PRADEEP PUBLICATION-INTEGRALS-EXERCISE
  1. True or False: int |x|dx=pmx^2/2+C

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  2. True or False: int 1/(2x)dx=1/2log|x|+C and int 1/(2x)dx=1/2log|2x|+C

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  3. True or False: underseta oversetb int f(x)dx ne underseta oversetb int...

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  4. True or False: underset(-pi/2)overset(pi/2)int sin^3xdx=0.

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  5. True or False: underseta oversetb int f(x)dx, if it exists, is a uniqu...

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  6. True or False: underset0overset(pi/2)int log|sinx|dx ne underset0overs...

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  7. True or False: If f(2a-x)=-f(x), then underset0overset(2a)int f(x)dx=0...

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  8. True or False: If f is an odd function defined on an interval [-a,a], ...

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  9. True or False: If f is a periodic function with period p, then underse...

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  10. True or False: underset0overset(2pi)int sin^2xdx=4 underset0overset(pi...

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  11. True or False: underset0oversetpi int cos^2xdx ne 2underset0overset(pi...

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  12. True or False: int tan^-1x dx=xtan^-1x-1/2log(1+x^2)+C.

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  13. True or False: underset0overset(pi/2)int (sin^6x)/(sin^6x+cos^6x)dx=pi...

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  14. True or False: underseta oversetbint (f(x))/(f(x)+f(a+b-x))dx=(a+b)/2

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  15. True or False: int 1/(1-2x)dx=-1/2log|2x-1|+C and also int 1/(1-2x)dx=...

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  16. True or False: underset0overset(pi)int xsinxdx ne pi

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  17. True or False: underset0 overset(pi/2)int x(sinx+cosx)dx=pi/2

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  18. True or False: int (x+1)^2dx=(x+1)^3/3+C and also int (x+1)^2dx=1/3x^3...

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  19. True or False: underset0 overset(pi)int cos^5 x dx ne 0

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  20. int (x-sin x)/(1-cos x)dx

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