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All the values of 'a' for which int(1)^(...

All the values of 'a' for which `int_(1)^(2) {a^(2)+(4-4a)x+4x^(3)}dxle12` 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-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 continuous function which is periodic with period 2...

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  3. All the values of 'a' for which int(1)^(2) {a^(2)+(4-4a)x+4x^(3)}dxle1...

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  4. Let f (x) be a function defined by f(x)=int(0)^(x) t(t^(2)-3t+2)dt, 1 ...

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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. If rArr int(0)^(1) (e^(-t))/(t+1) dt =a, "then"int(b-1)^(b) (e^(-1))/(...

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  9. If rArr int(-1)^(-4) f(x)dx= 4 and int(2)^(-4) (3-f(x))dx=7 , then the...

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

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

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  12. If [*] denots the greatest integer function then the value of the inte...

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  13. The value of int(0)^(100pi) sum(r=1)^(10) tan rx 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 I(n) int(-pi)^(pi) (sin nx)/((1+pi^(x))sinx)dx,n=0,1,2,... then whi...

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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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