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Let f: R to R and g: R to R be continuou...

Let `f: R to R and g: R to R` be continuous function. Then the value of the integral `int_(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)-g(-x)]dxi s` (a)`pi` (b) 1 (c) `-1` (d) 0

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Let f be an odd continous function which is periodic with priod 2 if g...

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  2. Evaluate inta^b(dx)/(sqrt(x)),w h e r ea , b > 0.

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  3. Let f: R to R and g: R to R be continuous function. Then the value of ...

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  4. Evaluate: int(-(3pi)/2)^(-pi/2)[(x+pi)^3+cos^2(x+3pi)]dx

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  5. Evaluate: int0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

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  6. Evaluate: int0^(100)x-[x]dx where [dot] represents the greatest in...

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  7. If Sn=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))] then (lim)(n...

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  8. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

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  9. The value of (int0^n[x]dx)/(int0^n{x}dx is (where [x] and {x} denotes ...

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  10. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

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  11. The value of int0^(pi/2)dx/(1+tan^3x) is

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  12. Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx

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  13. Let f be a contiuous function on [a,b]. If F(x)=(int(a)^(x)f(t)dt-int(...

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  14. Evaluate the following: int(-1)^(1)(sin x-x^(2))/(3-|x|)dx

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  15. If int(a)^(b)|sinx|dx=8 and int(0)^(a+b)|cosx|dx=9, then find the valu...

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  16. Evaluate: int(-pi/2)^(pi/2)sqrt(cos^(2n-1)x-cos^(2n+1)x)dx ,w h e r en...

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  17. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

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  18. Evaluate: int(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx

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  19. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

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  20. Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...

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