What is the area under the curve y = $x ^ { 3 }$ + x from x = 1 to x = 2?
A) $\frac { 21 } { 2 }$
B) $\frac { 6 } { 4 }$
C) $6 \frac { 1 } { 4 }$
D) $\frac { 21 } { 4 }$
E) none of these

Question

Quizplus · Accepted Answer

The area under the curve is found by integrating the function from 1 to 2. The integral of $x^3 + x$ is $\frac{x^4}{4} + \frac{x^2}{2}$. Evaluating this from 1 to 2 gives $\left(\frac{2^4}{4} + \frac{2^2}{2}\right) - \left(\frac{1^4}{4} + \frac{1^2}{2}\right) = \frac{21}{4}$.

What Is the Area Under the Curve Y = x3x ^ { 3 }x3

What Is the Area Under the Curve Y = $x ^ { 3 }$