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Consider the integrals I(1)=int(0)^(1)...

Consider the integrals
`I_(1)=int_(0)^(1)e^(-x)cos^(2)xdx,I_(2)=int_(0)^(1) e^(-x^(2))cos^(2)x dx,I_(3)=int_(0)^(1) e^(-x^(2))dx`
and `I_(4)=int_(0)^(1) e^(-x^(1//2)x^(2))dx`. The greatest of these integrals, is

A

`I_(1)`

B

`I_(2)`

C

`I_(3)`

D

`I_(4)`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
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  2. If I(1)=int(0)^(1) 2^(x^(2)) dx, I(2)=int(0)^(1) 2^(x^(3)) dx, I(3)=in...

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  3. Consider the integrals I(1)=int(0)^(1)e^(-x)cos^(2)xdx,I(2)=int(0)^(...

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  4. If f(x)=f(a+b-x) for all x in[a,b] and int(a)^(b) xf(x) dx=k int(a)^(b...

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  5. To find the numberical value of int(-2)^(2) (px^(3)+qx+8)dx it is nece...

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  6. Let f:R to R be continuous functions. Then the value of the integral i...

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  7. The value of int(-1//2)^(1//2) |xcos((pix)/(2))|dx is

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  8. The value of the integral int(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

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  9. The value of int(pi//2)^0 (1)/(9 cosx+12 sinx)dx is

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  10. If I=int(3)^(4) (1)/(3sqrt(logx))dxthen

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  11. If I=int(0)^(1//2) (1)/(sqrt(1-x^(2n)))dxthen which one of the follow...

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  12. If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dxthen which one of the foll...

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  13. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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  14. The value of the integral int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal...

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  15. If int(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint(0)^(oo) (log(1+x))/(1+x...

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  16. If int(log2)^(x) (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is equal to

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  17. The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

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  18. The integral int(0)^(pi) (1)/(a^(2)-2 a cos x+1)dx (a lt 1) is

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  19. The integral int(0)^(pi//2) f(sin 2 x)sin x dx is equal to

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  20. int(0)^(pi) k(pix-x^(2))^(100)sin2x" dx" is equal to

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