| Input |
|---|
| x^2 + 6 x + 7 |
| Geometric figure |
| parabola |
| Polynomial discriminant |
| Delta = 8 |
| Derivative |
| d/dx(x^2 + 6 x + 7) = 2 (x + 3) |
| Indefinite integral |
| integral (7 + 6 x + x^2) dx = x^3/3 + 3 x^2 + 7 x + constant |
| Global minimum |
| min{x^2 + 6 x + 7} = -2 at x = -3 |
| Definite integral |
| integral_(-3 – sqrt(2))^(-3 + sqrt(2)) (7 + 6 x + x^2) dx = -(8 sqrt(2))/3~~-3.77124 |
| Definite integral area below the axis between the smallest and largest real roots |
| integral_(-3 – sqrt(2))^(-3 + sqrt(2)) (7 + 6 x + x^2) theta(-7 – 6 x – x^2) dx = -(8 sqrt(2))/3~~-3.77124 |