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Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2...

Let `int _(0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = (lamda)/(mu)`
where `lamda and mu` are relatively prime positive integers. Find unit digit of `mu.

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VK JAISWAL-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. int( x^2+3)/(x^2+2)dx

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  2. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  3. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

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  4. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

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  5. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

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  6. Find the value of |a| for which the area of triangle included between ...

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  7. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

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  8. int( x^3)/(x^2-3)dx

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  9. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

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  10. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

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  11. int( x^3)/(x^2-2)dx

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  12. IF M be the maximum valur of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

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  13. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

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  14. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

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  15. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

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  16. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

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  17. If f (n)= 1/pi int (0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2)...

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  18. Let f (2-x) =f (2+xand f (4-x )= f (4+x). Function f (x) satisfies int...

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  19. Let l (n) =int (-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(2))/(3) + ........

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  20. int sqrt (x^2+4) dx

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