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I(1)=int(0)^((pi)/2)Ln (sinx)dx, I(2)=in...

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

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I_1=int_0^(pi/2)ln(sinx)dx ,I_2=int_(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then (a) I_1=2I_2 (b) I_2=2I_1 I_1=4I_2 (d) I_2=4I_1

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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

int_(0)^(pi//2)(x)/(sinx+cosx)dx .

Let I_(1)=int_(0)^(pi//4)e^(x^(2))dx, I_(2) = int_(0)^(pi//4) e^(x)dx, I_(3) = int_(0)^(pi//4)e^(x^(2)).cos x dx , then :

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  1. The value of int(-(pi/4)^(1/3))^((pi/4)^(1/3))(x^2)/((1+sin^2x^3)(1+e^...

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  2. If H is the orthocentre of a triangle ABC, then the radii of the cir...

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  3. I(1)=int(0)^((pi)/2)Ln (sinx)dx, I(2)=int(-pi//4)^(pi//4)Ln(sinx+cosx)...

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  4. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

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  5. Let (d)/(dx )F(x) =((e ^(sin x ))/(x )), x gt 0 If int(1 )^(4) (3)/(x)...

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  6. If in Delta ABC, (a -b) (s-c) = (b -c) (s-a), prove that r(1), r(2), r...

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  7. Show that int0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

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  8. If in triangle ABC (r)/(r(1))=(1)/(2), then the value of tan(A/2)(tan(...

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  9. Let u=int0^1("ln"(x+1))/(x^2+1)dx a n d v=int0^(pi/2)ln(sin2x)dx ,t h ...

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  10. A golf ball is dropped from a height of 80 m. Each time the ball hi...

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  11. if |f(x1)-f(x2)|<=(x1-x2)^2Find the equation of tangent to the curve y...

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  12. From the point (lambda,3) tangents are drawn to x^(2)/9+y^(2)/4=1 and ...

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  13. If a curve with equation of the form y=ax^(4)+bx^(3)+cx+d has zero gra...

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  14. A tangent is drawn to the ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costhet...

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  15. The left hand derivative of f(x)=[x]sin(pix) at x = k, k in Z, is

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  16. The locus of the point of intersection of the tangents at the extre...

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  17. Find the possible values of a such that f(x)=e^(2x)-(a+1)e^(x)+2xis mo...

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  18. The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is ...

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  19. Number of normals drawn from the point (-2,2) to the parabola y^2-2y-2...

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  20. Find two number whose sum is 100 and the sum of twice of first part an...

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