`int_0^1(a c x^(b+1)+a^3b x^(3b+5))dx`

int_(0)^(1)(x^(a)-b^(b))/(log x)dx

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

If int_(0)^(1)x^(11)e^(-x^(24))dx=A , and int_(0)^(1)x^(3)e^(-x^(8))dx=B , then the relation between A and B is

Evaluate I(b)=int_(0)^(1)(x^(b))dx=int_(0)^(1)(x^(b)-1)/("ln"x)dx,bge0 .

Evaluate I(b)=int_(0)^(1)(x^(b))dx=int_(0)^(1)(x^(b)-1)/("ln"x)dx,bge0 .