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Which of the following function (s) is/a...

Which of the following function (s) is/are even ?

A

`f (x ) = int _(0)^(x) ln (t + sqrt(1+t ^(2))) dt `

B

`g (x) =int _(0)^(x) ((2 ^(t) +1)t )/(2^(t) -1)dt `

C

`h (x) =int _(0)^(x ) (sqrt(1+t+t^(2))-sqrt(1-t +t^(2)))dt`

D

`l (x)= int _(0)^(x ) ln ((1-t)/(1+t))dt`

Text Solution

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The correct Answer is:
A, B, C, D
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VIKAS GUPTA (BLACK BOOK) ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. int (dx)/((1+sqrtx)^(8))=-(1)/(3(1+sqrtx)^(k(1)))+ (2)/(7(1+sqrtx)^(k(...

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  2. If int (-alpha) ^(alpha ) (e ^(x) + cos x ln (x + sqrt(1+x ^(2))))dx g...

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  3. "I f"intsqrt(x/(a^3-x^3))dx=d/bsin^(- 1)((x^(3/2))/(a^(3/2)))+C (wher...

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  4. Let int x sinx sec^3x dx = 1/2(x.f(x) - g(x)) + k, then

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  5. If int (sin 3 theta + sin theta ) cos theta e ^(sin theta ) d theta = ...

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  6. For a gt 0,if I= int sqrt((x)/(a ^(3) -x ^(3)))dx =A sin ^(-1) ((x ^(3...

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  7. If f (theta ) = lim (x to oo) sum ( r =o) ^(n theta) (2r)/(n sqrt((3 t...

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  8. If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/...

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  9. Let J=int (-1) ^(2) (cot ^(-1) ""(1)/(x )+ cot ^(-1) x ) dx, K =int (-...

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  10. Which of the following function (s) is/are even ?

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  11. Let lim(x->oo) sqrt((x-cos^2x)/(x+sinx)) and I2 = lim(h->0^+) int(-1)^...

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  12. For a gt 0,if I= int sqrt((x)/(a ^(3) -x ^(3)))dx =A sin ^(-1) ((x ^(3...

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  13. If int (dx)/(1- sin ^(4)x )= a tan x +b tan ^(-1) (c tan x )+ D, then...

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  14. The value of definite integral: int(-2014)^(2014)(dx)/(1+sin^(2015)x+s...

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  15. Let L= underset(nrarr infty)(lim)int(a)^(infty)(n dx)/(1+n^(2)x^(2)), ...

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  16. Let I =int (0)^(1 ) sqrt((1+sqrtx)/(1-sqrtx))dx and J = int (0)^(1 ) s...

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