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Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l...

`Ifint_0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint_(b-1)^b(e^(-t)dt)/(t-b-1)`

A

`ae^(-b)`

B

`-ae^(-b)`

C

`be^(b)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let t `=-u +b`. Then,
`rArr underset(0)overset(b)int (e^(-t))/(t-b-1) dt =underset(1)overset(0)int(e^(u-b))/(-u-1)(-du)`
`rArr underset(b-1)overset(b)int (e^(-t))/(t-b-1) dt =-underset(0)overset(1)int(e^(u-b))/(u+1)(-du)-e^(-b)underset(0)overset(1)intdu=ae^(-b)`
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer l...

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  2. rArrint(0)^(oo) [(2)/(e^(x))]dx (where [*] denotes the greatest intege...

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  3. Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...

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  4. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

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  5. For x epsilonR, and a continuous function f let I(1)=int(sin^(2)t)^(1+...

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  6. int(1)^(4) log(e)[x]dx equals

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  7. If [.] denotes greatest integer function, then the value of int(-pi//2...

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  8. int(0)^(100pi)(sum(r=1)^(10)tanrx)dx is equal to

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  9. If I(1)=int(0)^(pi//2) cos(sin x) dx,I(2)=int(0)^(pi//2) sin (cos x)...

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  10. For any n in N, the value of the intergral int(0)^(pi) (sin 2nx)/(sin...

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  11. For any n in N, int(0)^(pi) (sin^(2)nx)/(sin^(2)x)dx is equal to

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  12. For any n in N, int(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to

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  13. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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  14. If I(n)=int(0)^(pi//4) tan^(n)x dx, then (1)/(I(2)+I(4)),(1)/(I(3)+I...

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  15. Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x...

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  16. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

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  17. If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi...

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  18. If f(x) and g(x) are two continuous functions defined on [-a,a] then t...

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  19. Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f...

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  20. The value of the integral int(0)^(pi//2) sin 2n x cot x dx, where n ...

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