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].
-$$y = \frac { x } { 4 } + 2$$
A) $- \frac { b } { 4 } - 2$
B) $- \frac { b ^ { 2 } } { 8 } - 2 b$
C) $\frac { b ^ { 2 } } { 8 } + 2 b$
D) $\frac { b } { 4 } + 2$

Question

Quizplus · Accepted Answer

To find the area between the curve and x-axis on the interval [0, b], we need to integrate the equation with respect to x from 0 to b. 
$$\int_0^b (\frac{x}{4}+2) dx$$
Simplifying the integration: 
$$\frac{x^2}{8} + 2x \bigg]^b_0$$
Plugging in b and 0: 
$$\frac{b^2}{8} + 2b - (0^2/8 + 2(0)) = \frac{b^2}{8} + 2b$$
Therefore, the expression that represents the area of the region between the given curve and the x-axis on the interval [0, b] is $\frac { b ^ { 2 } } { 8 } + 2 b$ which is option C.

Use a Deﬁnite Integral to ﬁNd an Expression That Represents y=x4+2y = \frac { x } { 4 } + 2y=4x​+2

Use a Deﬁnite Integral to ﬁNd an Expression That Represents $y = \frac { x } { 4 } + 2$