Find the value of determinant.`|(a,h,g),(h,b,f),(g,f,c)|`

Let f(x) be a function satisfying f'(x)=f(x) with f(0) =1 and g(x) be a function that satisfies f(x) + g(x) = x^2 . Then the value of the integral int_0^1f(x) g(x) dx , is

If the angle between the two lines given by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 is (pi)/4 , then the contsntant a,b,h,g,f,c are related by

If f(x), g(x), h(x) are polynomials in x of degree 2 If F(x)=|[f,g,h],[f',g',h'],[ f'', g'', h'' ]| then F'(x) is

Let f,g and h be real-valued functions defined on the interval [0,1] by f(x)=e^(x^2)+e^(-x^2) , g(x)=x e^(x^2)+e^(-x^2) and h(x)=x^2 e^(x^2)+e^(-x^2) . if a,b and c denote respectively, the absolute maximum of f,g and h on [0,1] then

The value of int [f(x)g''(x) - f''(x)g(x)] dx is equal to

From the rate expression for the following reactions determine their order of reaction and the dimensions of the rate constants:- C_2H_5Cl(g)rarrC_2H_4(g) + HCl(g) Rate = k[C_2H_5Cl]