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I(1)=int(0)^((pi)/2)(sinx-cosx)/(1+sinxc...

`I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx`,
`I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx`. Then

A

`l_(1)=l_(2)=l_(3)=l_(4)=0`

B

`l_(1)=l_(2)=l_(3)=0` but `l_(4) ne 0`

C

`l_(1)=l_(3)=l_(4)=0` but `l_(2) ne 0`

D

`l_(1)=l_(4)=0` but `l_(3) ne 0`, and `l_(2) ne 0`

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I_1=int_0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I_2=int_0^(2pi)cos^6xdx ,I_3=int_(pi/2)^(pi/2)sin^3xdx ,I_4=int_0^1 1n(1/x-1)dxdotT h e n I_2=I_3=I_4=0,I_1!=0 I_1=I_2=I_3=0,I_4!=0 I_1=I_2=I_3=0,I_4!=0 I_1=I_4=I_3=0,I_2!=0

If I_(1)=int_(0)^(2pi)sin^(3)xdx and I_(2)=int_(0)^(1)ln((1)/(x)-1)dx , then

I_(1)=int_(0)^((pi)/2)Ln (sinx)dx, I_(2)=int_(-pi//4)^(pi//4)Ln(sinx+cosx)dx . Then

If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx

int_(0)^(pi)(x)/(1+sinx)dx .

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^(-(1//2)x^(2))dx . The greatest of these integrals, is

int_(0)^(pi//4)(dx)/((1+cos2x))

int_(0)^(pi//2) sqrt(1- cos 2x) dx

int_(0)^(pi//2) sqrt(1- cos 2x) dx

AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (Only one answer)
  1. Find the value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx, agt0.

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  2. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...

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  3. I(1)=int(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I(2)=int(0)^(2pi)cos^(...

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  4. Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" an...

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  5. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

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  6. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

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  7. Value of the definite integral int(-1/2)^(1/2)(sin^(- 1)(3x-4x^3)-cos^...

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  8. Let f(x)=int(0)^(x)(sin^(100)t)/(sin^(100)t+cos^(100)t)dt, then f(2pi)...

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  9. int(0)^(pi)(x.sin^(2)x.cosx)dx is equal to

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  10. int0^1000 e^(x-[x])dx

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  11. The value of the definite integral int(19)^37((x)^2+3(sin2pix))dx wher...

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  12. If l(n)=int(0)^((pi)/(4)) tan^(n) xdx show that (1)/(l(2)+l(4)),(1)/(l...

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  13. The value of ("lim")(n rarr oo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r...

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  14. underset(kto0) lim1/kint0^k(1+sin2x)^(1/x)dx

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  15. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  16. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

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  17. If f(x)=[{:(sqrt(1-x), , , 0 le x le 1),((7x-6)^(-1) , , ,1 le x le 2)...

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  18. If f:RrarrR defined by f(x)=sinx+x, then find the value of int0^pi(f^-...

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  19. The value of int0^100 [tan^-1 x]dx is, (where [*] denotes greatest in...

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  20. Iff(x)={0,w h e r ex=n/(n+1),n=1,2,31,e l s e w h e r e t h e nt h ev...

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