Use a deﬁnite integral to ﬁnd an expression that represents the area of the region between the given curve and the
x-axis on the interval [0, b].
-$$\mathrm { y } = 24 \mathrm { x } ^ { 2 }$$
A) $- 48 \mathrm {~b}$
B) $8 \mathrm {~b} ^ { 3 }$
C) $48 \mathrm {~b}$
D) $- 8 b ^ { 3 }$

Question

Quizplus · Accepted Answer

The area under the curve $y = 24x^2$ from $x = 0$ to $x = b$ is found using the definite integral $\int_{0}^{b} 24x^2 dx$. Solving this integral gives $\frac{24}{3}x^3$ evaluated from 0 to b, which simplifies to $8b^3$.

Use a Deﬁnite Integral to ﬁNd an Expression That Represents y=24x2\mathrm { y } = 24 \mathrm { x } ^ { 2 }y=24x2

Use a Deﬁnite Integral to ﬁNd an Expression That Represents $\mathrm { y } = 24 \mathrm { x } ^ { 2 }$