Integrate the following: `ax^2 +bx+c`

Find (dy)/(dx) for the following : y=ax^(2)+bx+c

Find (dy)/(dx) for the following : y=sqrt(ax^(2)+bx+c)

Integral of the form sqrt(ax^(2)+bx+cdx)

Let f(X) = ax^(2) + bx + c . Consider the following diagram .

int (ax^(2)+bx+c)dx

Which one of the following is the equation whose roots are respectively three xx the roots of the equation ax^(2)+bx+c=0 a) ax^(2)+3bx+c=0 b) ax^(2)+3bx+9c=0 c) ax^(2)-3bx+9c=0 d) ax^(2)+bx+3c=0

Integral of the form (px+q)sqrt(ax^(2)+bx+c)dx

Euler's substitution: Integrals of the form intR(x, sqrt(ax^(2)+bx+c))dx are claculated with the aid of one of the following three Euler substitutions: i. sqrt(ax^(2)+bx+c)=t+-x sqrt(a)if a gt 0 ii. sqrt(ax^(2)+bx+c)=tx+-x sqrt(c)if c gt 0 iii. sqrt(ax^(2)+bx+c)=(x-a)t if ax^(2)+bx+c=a(x-a)(x-b) i.e., if alpha is real root of ax^(2)+bx+c=0 int(xdx)/((sqrt(7x-10-x^(2)))^(3)) can be evaluated by substituting for x as