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The natural number nle5 for which In=int...

The natural number `nle5` for which `I_n=int_0^1 e^x(x-1)^n dx=16-6e` is

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int_0^(100)e^(x-[x])dx=

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Determine a positive integer nle5 such that, int_(0)^(1)e^(x)(x-1)^(n)dx=16-6e .

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The numbers of possible continuous f(x) defined in [0,1] for which I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e 1 (b) oo (c) 2 (d) 0

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Ifint0^oo(x^2dx)/((x^2+a^2)(x^2+b^2)(x^2+c^2)) =pi/(2(a+b)(b+c)(c+a...

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  2. The value of the integral int0^1(dx)/(x^2+2xcosalpha+1) is equal to ...

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  3. The natural number nle5 for which In=int0^1 e^x(x-1)^n dx=16-6e is

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  4. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

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  5. If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), th...

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  6. Evaluate: int0^(1)sin^(-1)((2x)/(1+x^2))dx

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  7. Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...

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  8. L e t \ f(n)=1+1/2+1/3+...+1/n. Then show that f(n)=int0^(pi/2)cot(the...

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  9. Let f(x) be a continuous function AAx in R , except at x=0, such that...

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  10. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

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  11. Determine a positive integer n such that int0^(pi/2)x^nsinx dx=3/4(pi^...

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  12. f,g,h are continuous in [0,a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5...

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  13. If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...

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  14. Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...

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  15. Evaluate: int3^10[log[x]]dx

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  16. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

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  17. The value of int0^1(x^4(1-x)^4)/(1+x^2)dx is/are (a)(22)/7-pi (b)...

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  18. Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...

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  19. Evaluate:int-pi^pi ((2x)(1+sinx)/(1+cos^2x))dx

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  20. Q. if int0^100(f(x) dx = a, then sum(r=1)^100(int0^1( f(r-1+x)dx))=

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