Question

Evaluate. Then interpret the result in terms of the area above and/or below the x-axis. 1 2 f (x² – 3x) dx -1 1 S (33 – 3x) dx = (Type an integer or a simplified fraction.) -1

Answer 1

Calculate the value of

$\int (x^3-3x)dx$$\int (x^3-3x)dx=\frac{x^4}{4}-\frac{3x^2}{2}$

Apply the limits implies,

$\begin{gathered} \int ^{\frac{1}{2}}_{-1}(x^3-3x)dx=\lbrack\frac{x^4}{4}-\frac{3x^2}{2}\rbrack^{\frac{1}{2}}_{-1} \\ =\frac{1}{64}-\frac{3}{8}-\frac{1}{4}+\frac{3}{2} \\ =\frac{57}{64} \end{gathered}$

Therefore, the answer is 0.89.

Nearest integer is 1.