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Consider the function f(x) satisfying th...

Consider the function `f(x)` satisfying the relation `f(x+1)+f(x+7)=0AAx in Rdot` STATEMENT 1 : The possible least value of `t` for which `int_a^(a+t)f(x)dx` is independent of `ai s12.` STATEMENT 2 : `f(x)` is a periodic function.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. STATEMENT 1 : On the interval [(5pi)/4,(4pi)/3]dot the least value of ...

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  2. Evaluate: int0^(10pi)[tan^(-1)x]dx ,w h e r e[x] represents greatest ...

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  3. Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx ...

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  4. Evaluate: int0^((5pi)/(12))[tanx]dx , where [dot] denotes the grea...

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  5. Consider I1=int0^(pi//4)e^(x^2)dx ,I2=int0^(pi//4)e^x dx ,I3=int0^(pi/...

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  6. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

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  7. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

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  8. if [x] denotes the greatest integer less than or equal to x then integ...

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  9. The value of int0^(2pi)[2sinx]dx ,w h e r e[dot] represents the great...

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  10. f(x)=int1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f...

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  11. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)])dx , ...

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  12. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

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  13. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

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  14. If g(x)=int0^xcos^4tdt , then g(x+pi) equals (a)g(x)+g(pi) (b) g(...

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  15. Evaluate lim(x to 4)int4^x((4t-f(t)))/((x-4))dt

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  16. Evaluate: int(pi/4)^((3pi)/4)dx/(1+cosx)

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  17. If In=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))is equal to

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  18. Let f be a one-to-one continuous function such that f(2)=3 and f(5)=7....

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  19. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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  20. Evaluate: int0^(e-1)(e^((x^2+2x-1)/2))/(x+1)dx+int1^e xlogx e^(x^(2-2)...

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