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Show that int0^1(dx)/(1+x^6)>pi/4...

Show that `int_0^1(dx)/(1+x^6)>pi/4`

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Explore conceptually related problems

Show that :int_(0)^(1)(log x)/((1+x))dx=-int_(0)^(1)(log(1+x))/(x)dx

(i) Show that int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx. (ii) Find the value of int_(-1)^(3//2)|x sin pix|dx .

int_(0)^(pi) dx/(1-sin x)=

int_0^(pi/2) (dx)/(1+cos x)

If|a|lt 1, show that int _(0)^(pi)(log(1+a cos x ))/( cos x)dx =pi sin^(-1) a

If [x] denotes the integral part of [x] , show that: int_0^((2n-1)pi) [sinx]dx=(1-n)pi,n in N

Show that: int_0^1 tan^-1x/xdx=1/2int_0^(pi/2) ycosecy dy

int_0^pi x/(1+sin x) dx

(i) int_0^1 (dx)/sqrt(1-x^2) (ii) int_0^1 (dx)/sqrt(1+x^2) (iii) a int_1^sqrt3 (dx)/(1+x^2) b int_0^1 (dx)/(1+x^2) (iv) int_0^(2//3) (dx)/(4+9x^2) (v) int_0^1 x/(x^2+1)dx (vi) int_2^3 x/(x^2+1) dx

BANSAL-INTEGRALS-All Questions
  1. Evaluate : (lim)(x->0)(int0xtanx\ dx)/(xtanx)

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  2. Find the points of maxima of f(x)=int0^(x^2)(t^2-t)/(e^t+1)dtdot

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  3. Show that int0^1(dx)/(1+x^6)>pi/4

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  4. If int0^(10)f(x)dx=5, find the value of sum(k=1)^(10)int0^1f(k-1+x)dxd...

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  5. If y(x)=int(pi^2/16)^(x^2) (cosx cos sqrt(theta))/(1+sin^2 sqrt(theta)...

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  6. If In=int0^(pi//4)tan^n x dx , show that 1/(I2+I4),1/(I3+I5),1/(I4+...

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  7. Evaluate: lim(n->oo)[1/((n+1)^2\ )+1/((n+2)^2)+...+1/((2n)^2)]

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  8. Evaluate: inta^b e^x dx using limit of sum

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  9. Evaluate : (lim)(n->oo)sum(r=1)^n1/((n^2+r^2)^(1//2))

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  10. Evaluate the following definite integrals: int0^(pi//4)(sqrt(1-sin2...

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  11. Evaluate the following definite integrals: int0^(pi//2)xsinx sin2x d...

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  12. int0^(2pi)(dx)/(2+sin2x)

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  13. Evaluate the following definite integrals: int(1//e)^e|l\ n x|dx

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  14. Evaluate the following definite integral: int0^(pi//2)(sinx+cos x)dx

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  15. Evaluate the following definite integrals: int0^1(e^(-x))/(1+e^x)dx

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  16. Evaluate the following definite integrals: int0^(pi//4)(sinx+cosx)/...

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  17. The value of int-pi^pi cos^2x/[1+a^x].dx,a>0 is

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  18. For a positive integer n, let I (n) int (-pi)^(pi) ((pi)/(2) -|x|) cos...

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  19. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

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  20. Find the limit, when n->oo,\ of\ [((n^3+1^3)(n^3+2^3)(n^3+3^3).........

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