Select all expressions matching the value of the definite integral int _(-1)^1(3x^2-1)dx 2 0 0.5

To find the value of the definite integral $\int _{-1}^{1}(3x^{2}-1)dx$, we need to evaluate the integral.<br /><br />First, let's integrate the function $3x^2 - 1$ with respect to $x$:<br /><br />$\int (3x^2 - 1)dx = x^3 - x + C$<br /><br />Now, we can evaluate the definite integral by substituting the upper and lower limits of integration:<br /><br />$\int _{-1}^{1}(3x^{2}-1)dx = [(1)^3 - (1)] - [(-1)^3 - (-1)]$<br /><br />Simplifying the expression:<br /><br />$\int _{-1}^{1}(3x^{2}-1)dx = (1 - 1) - ((-1) - (-1))$<br /><br />$\int _{-1}^{1}(3x^{2}-1)dx = 0 - 0$<br /><br />$\int _{-1}^{1}(3x^{2}-1)dx = 0$<br /><br />Therefore, the correct answer is 0.