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lim(nto oo) (1)/(n^(2))sum(r=1)^(n) re^(...

`lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=`

A

0

B

1

C

e

D

2e

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B
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If f(x) is integrable over [1,], then int_(2)^(2)f(x)dx is equal to lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)f((r)/(n))lim_(n rarr oo)(1)/(n)sum_(r=n+1)^(2n)f((r)/(n))lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)f((r+n)/(n))lim_(n rarr oo)(1)/(n)sum_(r=1)^(2n)f((r)/(n))

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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. int(-pi//2)^(pi//2) sin^(2)x cos^(2) x(sin x+cos x)dx=

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  2. lim(nto oo) (1)/(n^(2))sum(r=1)^(n) re^(r//n)=

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  3. The value of the integral int(-1)^(1) sin^(11)x" dx" is

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  4. The value of int(-pi)^(pi)(1-x^(2)) sin x cos^(2) x" dx", is

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  5. int(-pi)^(pi) [cos px-sin qx]^(2) dx where p,q are integers is equal t...

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  6. If int(0)^(pi//3) (cos x)/(3+4 sin x)dx=k log ((3+2sqrt(3))/(3)), then...

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  7. The value of int(3)^(5) (x^(2))/(x^(2)-4)dx, is

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  8. The greater value of (x)=int(-1//2)^(x) |t|dt on the interval [-1//2,1...

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  9. f(x)={:{(1-x","" "0 le c le 1),(0","" "1 le x le 2" and "phi ...

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  10. If f(x)=int(x)^(-1) |t|dt, then for any x ge 0, f(x) equals

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  11. int0^(2) (x-log(2)a)dx=2 log((2)/(a)), if

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  12. If int(1)^(a) (a-4x)dx ge 6-5a, a gt 1, then a equals

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  13. The value of int1^2 {f(g(x))}^(-1)f'(g(x))g'(x) dx , where g(1)=g(2),...

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  14. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  15. The solution of the equation int(log(2))^(x) (1)/(e^(x)-1)dx=log(3)/(2...

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  16. If int(a)^(b) (x^(n))/(x^(n)+(16-x)^(n))dx=6, then

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  17. Let m be any integer. Then, the integral int(0)^(pi) (sin 2m x)/(sin x...

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  18. int(-pi//4)^(pi//4) e^(-x)sin x" dx" is

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  19. (d)/(dx)(f(x))=phi(x)" for "a lex le b,int(a)^(b) f(x)phi(x)dx=

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  20. int(-pi//2)^(pi//2) (cos x)/(1+e^(x))dx=

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