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If `f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int_(0)^(2) x^(2)f(x)dx` is equal to

A

1

B

`(4)/(3)`

C

`(5)/(3)`

D

`(5)/(2)`

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of the integral int(0)^(pi)x log sin x dx is

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  2. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)underset(0)overset(oo)in...

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  3. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

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  4. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

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  5. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

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  6. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

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  7. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

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  8. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

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  9. The value of the integral int 0^oo 1/(1+x^4)dx is

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  10. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

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  11. The value of alpha in [0,2pi] which does not satify the equation int(p...

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  12. lim(x to 0)(int(0)^t(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

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  13. If x satisfies the equation x^(2)( int(0)^(1) (dt)/(t^(2)+ 2t cos al...

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  14. The value of alpha in (-pi, 0) satisfying sin alpha+int(alpha)^(2alpha...

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  15. The value of int(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx i...

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  16. The value of int(0)^(pi) (1)/(5+3cosx)dx, is

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  17. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  18. lim(n to oo) sum(r=1)^(n) {(r^(3))/(r^(4)+n^(4))} equals

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  19. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  20. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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