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Let f(x) = {{:(1-x ,"If" 0 le x le 1),(0...

Let `f(x) = {{:(1-x ,"If" 0 le x le 1),(0, "if" 1 lt x le 2),((2-x)^(2),"if"2 lt x le 3):}` and function `F(x) = underset(0)overset(x)intf(t) dt`. If number of points of discountinuity in [0,3] and non-differentiablity in (0,2) and `F(x)` are `alpha` and `beta` respectively , then `(alpha - beta)` is equal to .

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The correct Answer is:
`(pi ^(2))/(6 sqrt3)`
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MOTION-DEFINITE INTEGRATION -EXERCISE -3
  1. Evaluate lim ( n to oo) sum( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2))...

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  2. lim(n->oo) 3/n[1+sqrt(n/(n+3)) + sqrt(n/(n+6)) + sqrt(n/(n+9)) +.........

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  3. Evaluate lim ( n to oo) 1/n [ (1)/( n + 1)+ (2)/(n + 2)+...+ (3n )/(...

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  4. Evaluate: ("lim")(nvecoo)[(n !)/(n^n)]^(1//n)

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  5. Dupose g(x) is the inverse of f (x) and f (x) has a domain x in [a,b]....

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  6. lf f(x) = 5^(g(x)) and g(x)=int2^(x^2)t/(ln(1+t^2) dt, then find the v...

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  7. Solve the equation for y as a function of x, satisfying x . int (0) ...

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  8. Evaluate. I = int (0) ^(1) 2 sin (pt) sin (qt) dt. If : p & q are di...

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  9. Evaluate. I = int (0) ^(1) 2 sin (pt) sin (qt) dt. If : p & q are eq...

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  10. int(0)^(pi//2) sin 2x tan^(-1) (sinx)dx =

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  11. Let f and g be function that are differentiable for all real numbers x...

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  12. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

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  13. If n>1, then int0^oo(dx)/((x+sqrt(1+x^2))^n) equals

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  14. Evaluate : int0^1(sin^(- 1)sqrt(x))/(x^2-x+1)dx

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  15. Let f(x) = {{:(1-x ,"If" 0 le x le 1),(0, "if" 1 lt x le 2),((2-x)^(2)...

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  16. Let u=int0^(pi/4)((cosx)/(sinx+cosx))^2dx and v=int0^(pi/4)((sinx+cosx...

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  17. The value of int(-2)^(0) [x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)]dx is equal...

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  18. If function f(x) is continuous in the interval (a, b) and having same ...

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  19. If function f(x) is continuous in the interval (a, b) and having same ...

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  20. If function f(x) is continuous in the interval (a, b) and having same ...

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