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VIKAS GUPTA (BLACK BOOK)-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
- int (dx)/((1+sqrtx)^(8))=-(1)/(3(1+sqrtx)^(k(2)))+ (2)/(7(1+sqrtx)^(k(...
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- If int (-alpha) ^(alpha ) (e ^(x) + cos x ln (x + sqrt(1+x ^(2))))dx g...
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- "I f"intsqrt(x/(a^3-x^3))dx=d/bsin^(- 1)((x^(3/2))/(a^(3/2)))+C (wher...
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- Let int x sinx sec^3x dx = 1/2(x.f(x) - g(x)) + k, then
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- If int(sin3theta+sintheta)costhetae^sinthetadtheta=(Asin^3theta+Bcos^2...
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- For a gt 0, if I = int sqrt((x)/(a ^(3) -x ^(3)))dx = A sin ^(-1) ((x ...
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- If f (theta ) = lim (x to oo) sum ( r =o) ^(n theta) (2r)/(n sqrt((3 t...
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- 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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- Let J=int (-1) ^(2) (cot ^(-1) ""(1)/(x )+ cot ^(-1) x ) dx, K =int (-...
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- Which of the following function (s) is/are even ?
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- Let lim(x->oo) sqrt((x-cos^2x)/(x+sinx)) and I2 = lim(h->0^+) int(-1)^...
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- For a gt 0, if I = int sqrt((x )/(a ^(3) -x ^(3)))dx =A sin ^(-1) ((x...
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- If int (dx)/(1- sin ^(4)x )= a tan x +b tan ^(-1) (c tan x )+ D, then...
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- The value of definite integral: int(-2014)^(2014)(dx)/(1+sin^(2015)x+s...
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- Let L= underset(nrarr infty)(lim)int(a)^(infty)(n dx)/(1+n^(2)x^(2)), ...
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- Let I =int (0)^(1 ) sqrt((1+sqrtx)/(1-sqrtx))dx and J = int (0)^(1 ) s...
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