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If f(n)=int0^x[cos t]dt, where x in (2 n...

If `f(n)=int_0^x[cos t]dt,` where `x in (2 npi,2 npi+pi/2); n in N and [*]` denotes the greatest integer function. Then, the value of `|f(1/pi)|` is ...

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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 3
  1. The value of int(-1)^(3){|x-2|+[x]} dx, where [.] denotes the greatest...

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  2. The value of int(-1)^(3)(|x|+|x-1|) dx is equal to

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  3. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

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  4. The value of int(0)^(2)[x+[x+[x]]] dx (where, [.] denotes the greates...

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  5. The value of int0^([x]) 2^x/(2^([x])) dx is equal to (where, [.] denot...

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  6. The value of int(0)^(4) {x} dx (where , {.} denotes fractional part of...

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  7. The value of int(1)^(4){x}^([x]) dx (where , [.] and {.} denotes the g...

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  8. The value of int(0)^(x)[t+1]^(3) dt (where, [.] denotes the greatest ...

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  9. The value of int(0)^(10pi)[tan^(-1)x]dx (where, [.] denotes the greate...

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  10. If f(x)=min{|x-1|,|x|,|x+1|, then the value of int-1^1 f(x)dx is equal...

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  11. The value of int(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greate...

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  12. The value of int(1)^(10pi)([sec^(-1)x]) dx (where ,[.] denotes the gre...

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  13. The value of int(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes gr...

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  14. The value of int0^(pi/4)(tan^n(x-[x])+tan^(n-2)(x-[x]))dx (where, [*] ...

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  15. The value of int(0)^(2)[x^(2)-x+1] dx (where , [.] denotes the greates...

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  16. Evaluate int0^a[x^n]dx, (where,[*] denotes the greatest integer functi...

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  17. Prove that int(0)^(x) [x]dx=[x]([x]-1)/(2)+[x] (x-[x]), where [.] deno...

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  18. If f(n)=(int0^n[x]dx)/(int0^n{x}dx)(where,[*] and {*} denotes greatest...

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  19. If f(n)=int0^x[cos t]dt, where x in (2 npi,2 npi+pi/2); n in N and [*]...

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  20. If int0^x[x]dx=int0^([x]) xdx,x !in integer (where, [*] and {*} denote...

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