Evaluate the integral.
-$$\int _ { 2 } ^ { \sqrt { 17 } } x d x$$
A) 13
B) $- \frac { 13 } { 2 }$
C) $\frac { 13 } { 2 }$
D) $\sqrt { 17 } - 2$

Question

Quizplus · Accepted Answer

We can evaluate the integral using the formula for the integral of a power function:
$$\int x^n dx = \frac{x^{n+1}}{n+1}+C$$
In this case, we have $n=1$, so
$$\int _ { 2 } ^ { \sqrt { 17 } } x d x = \frac{x^{2}}{2} \Bigg|_{2}^{\sqrt{17}}$$
Plugging in the limits of integration and simplifying, we get
$$\frac{(\sqrt{17})^2}{2} - \frac{2^2}{2} = \frac{17-4}{2} = \frac{13}{2}$$
Therefore, the answer is C.

Evaluate the Integral ∫217xdx\int _ { 2 } ^ { \sqrt { 17 } } x d x∫217​​xdx

Evaluate the Integral $\int _ { 2 } ^ { \sqrt { 17 } } x d x$