Compute the deﬁnite integral as the limit of Riemann sums.
-$$\int _ { - 3 } ^ { 3 } x ^ { 3 } d x$$
A) $\frac { 81 } { 2 }$
B) 27
C) 0
D) $\frac { 81 } { 4 }$

Question

Quizplus · Accepted Answer

The function $x^3$ is an odd function, meaning that for every positive value of $x$, there is a corresponding negative value of $x$ that gives the opposite value of the function. When integrating an odd function over a symmetric interval around zero, the positive and negative areas cancel out, resulting in an integral of 0.

Compute the Deﬁnite Integral as the Limit of Riemann Sums ∫−33x3dx\int _ { - 3 } ^ { 3 } x ^ { 3 } d x∫−33​x3dx

Compute the Deﬁnite Integral as the Limit of Riemann Sums $\int _ { - 3 } ^ { 3 } x ^ { 3 } d x$