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

If int_-2^-1 (ax^2-5)dx=0 and 5 + int_1^2 (bx + c) dx = 0 , then

int (ax +b)^(2)dx

Solve: 1. int_0^3(ax^2+bx+c)dx 2. int_-1^1e^xdx 3. int_(-pi//2)^(pi//2) cosx dx 4. int_0^10sec^2(3x+6)dx

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P

If alpha, beta are the roots of the equation ax^(2) +2bx +c =0 and alpha +h, beta + h are the roots of the equation Ax^(2) +2Bx + C=0 then

if alpha&beta are the roots of the quadratic equation ax^2 + bx + c = 0 , then the quadratic equation ax^2-bx(x-1)+c(x-1)^2 =0 has roots

Evaluate int_(1)^(4) (ax^(2)+bx+c)dx .

If int_0^3 (3ax^2+2bx+c)dx=int_1^3 (3ax^2+2bx+c)dx where a,b,c are constants then a+b+c=

int(ax^3+bx^2+cx+d)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 (xdx)/(sqrt(7x-10-x^(2))^3) can be evaluated by substituting for x as