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prove it 2e^(-1/4) < int0^2e^(x^2-x)dx <...

prove it `2e^(-1/4) < int_0^2e^(x^2-x)dx < 2e^2`

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MOTION-DEFINITE INTEGRATION -EXERCISE -3
  1. Prove that 4le int(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30.

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  2. Prove that pi/6<int0^1(dx)/(sqrt(4-x^2-x^3))<pi/(4sqrt(2))

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  3. prove it 2e^(-1/4) < int0^2e^(x^2-x)dx < 2e^2

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  4. If a lt overset(2pi)underset(0)int (1)/(10+3 cos x)dx lt b. Then the o...

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  5. Prove the inequalities 1/2 le int (0) ^(2) (dx)/(2+x ^(2)) le 5/6

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  6. Evaluate lim ( n to oo) sum( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2))...

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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