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int0^1f(x)dx=1,\ int0^1xf(x)dx=a ,\ int0...

`int_0^1f(x)dx=1,\ int_0^1xf(x)dx=a ,\ int_0^1x^2f(x)dx=a^2,\ t h e n\ int_0^1(a-x)^2f(x)dx` equals a. `4a^2` b. `0` c. `2a^2` d. none of these

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. The value of int0^(pi//2)cosx\ e^(sin x)dx\ i s a. 1 b. e-1 c. 0 d. -...

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  2. If int0^a1/(1+4x^2)dx=\ pi/8 , then a equals a.pi/2 b. pi/4 c. 1/2 d. ...

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  3. int0^1f(x)dx=1,\ int0^1xf(x)dx=a ,\ int0^1x^2f(x)dx=a^2,\ t h e n\ int...

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  4. The value of int(-pi)^pisin^3xcos^2x\ dx\ is a.(pi^4)/2 b. (pi^4)/4 c...

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  5. int(pi//6)^(pi//3)1/(sin2x)dx\ is equal to a. (log)e3 b. (log)"e"sqr...

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  6. int(-1)^1|1-x|dx is equal to a.-2 b. 2 c. 0 d. 4

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  7. int0^1x/((1-x)^(54))dx= a. 9(pi/2)^9 b. 10(pi/2)^9 c. (pi/2)^9 d....

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  8. (lim)(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} a. I n\ (1/3) b. I n\ (2/3)...

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  9. The value of the integral int(-2)^2|1-x^2|dx is a.4 b. 2 c. -2 d. 0

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  10. int0^(pi//2)1/(1+cot^3x)dx is equal to a 0 b. 1 c. pi//2 d. pi//4

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  11. int0^(pi//2)(sinx)/(sin x+cos x)dx equals to a. pi//2 b. pi//4 c. pi//...

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  12. int0^(pi//2)xsinx\ dx is equal to a. pi//2 b. pi//4 c. pi d. 1

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  13. int0^(pi//2)sin2xlogtanx\ dx\ is equal to a. pi//2 b. pi c. 0 d. 2pi

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  14. The value of int0^pi1/(5+3cosx)dx is a. pi//2 b. pi//4 c. 0 d. pi...

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  15. Evaluate:int0^oolog(x+1/x)(dx)/(1+x^2)

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  16. int0^(2a)f(x)dx is equal to a.2int0^af(x)dx b. 0 c. int0^af(x)dx+...

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  17. If f(a+b-x)=f(x),\ t h e n\ inta^b xf(x)dx is equal to a.(a+b)/2inta^...

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  18. The value of int0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ is a.1 b. -1 c....

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  19. Choose the correct answer The value of int0pi/2log((4-3sinx)/(4+3cosx)...

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  20. The value of int(-pi//2)^(pi//2)(x^3+x\ cos x+tan^5x+1)dx , is a. 2 b....

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