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Let f be a continuous function on [a ,b]...

Let `f` be a continuous function on `[a ,b]dot` Prove that there exists a number `x in [a , b]` such that `int_a^xf(t)dt=int_x^bf(t)dtdot`

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The correct Answer is:
`int_(a)^(x) f(t) dt= int _(x)^(b) f(t) dt` for alteast one value of `x in [a,b]`.
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
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  3. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

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  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  9. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

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  10. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

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  11. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  12. Match the conditions/ expressions in Column I with statement in Column...

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  13. Find x+y+z

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  14. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

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  15. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  16. The value of int(In2)^(In3) (x sinx)dx is

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  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

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  18. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx is (are)

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  19. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^...

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  20. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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  21. Which of the following is true?

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