Question

Evaluate the definite integral:

∫−4−7(x−1+3x)dx=

Answer 1

$\int_{-4}^{-7} (x - 1 + 3x)dx\\ Solution:\\ \left[\LARGE{\frac{x^{1+1}}{1 + 1} - 1x + 3\frac{x^{1+1}}{1 +1}}\right]_{-4}^{-7}\\ \left[\LARGE{\frac{x^{2}}{2} - 1x + 3\frac{x^{2}}{2}}\right]_{-4}^{-7}\\ \left[\LARGE{\frac{x^{2}}{2} + 3\frac{x^{2}}{2} -x}\right]_{-4}^{-7}\\ \left[\LARGE{4\frac{x^{2}}{2} -x}\right]_{-4}^{-7}\\ \left[\LARGE{\frac{4x^2 - 2x}{2}}\right]_{-4}^{-7}\\ \left(\LARGE{\frac{4(-7)^2 - 2(-7)}{2}}\right) - \left(\LARGE{\frac{4(-4)^2 - 2(-4)}{2}}\right)\\ 105 - 36\\ = 69$