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All the value of d for which int(1)^(2...

All the value of d for which
`int_(1)^(2){a^(2)+(4-4a)x+4x^(3)} d xle12` are given by

A

a=3

B

`a le4`

C

`0 le a le3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`underset(1)overset(2)int{a^(2)+(4-4a)x+4x^(3)}dxle12`
`rArr [a^(2)+(2-2a)x^(2)+x^(4)]_(1)^(2) le12`
`rArr a^(2)+(2-2a)(4-1)+(16-1)le 12`
`rArr a^(2)+6-6a+15le12`
`rArr a^(2)-6a+9 le0 rArr (a-3)^(2) le0 rArr a=3`
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. If | int(a)^(b) f(x)dx|= int(a)^(b)|f(x)|dx,a ltb,"then " f(x)=0 has

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  2. Let f(x) be an odd continous function which is periodic with period 2....

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  3. All the value of d for which int(1)^(2){a^(2)+(4-4a)x+4x^(3)} d xle1...

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  4. Let f(x) be a function defined by f(x)=int(1)^(x)t(t^(2)-3t+2)dt,1ltxl...

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  5. If int(0)^(x){t}dt=int(0)^({x})t dt ("where" x gt0 neZ and and {*} rep...

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  6. Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer l...

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

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

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

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

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

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

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

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

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

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

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

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

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