Provide an appropriate response.
-Suppose we wish to use a substitution to find $\left(x^{2}+2\right) d x$, and we let $u=x^{2}+2$. Which of the following would be the correct results?
i. $\int u d u$
ii. $\int\left(\frac{u}{2}\right) d u$
iii. $\int(u-2) d u$

A) Both i and iii
B) Only i
C) Only ii
D) None of these is correct.

Question

Provide an appropriate response.
-Suppose we wish to use a substitution to find $\left(x^{2}+2\right) d x$, and we let $u=x^{2}+2$. Which of the following would be the correct results?
i. $\int u d u$
ii. $\int\left(\frac{u}{2}\right) d u$
iii. $\int(u-2) d u$

A) Both i and iii
B) Only i
C) Only ii
D) None of these is correct.

Quizplus · Accepted Answer

The substitution $u = x^2 + 2$ implies $du = 2x \, dx$, so $dx = \frac{du}{2x}$. The expression $(x^2 + 2) dx$ cannot be directly rewritten as any of the given integrals without further manipulation or additional information.

Provide an Appropriate Response (x2+2)dx\left(x^{2}+2\right) d x(x2+2)dx , and We Let u=x2+2u=x^{2}+2u=x2+2

Provide an Appropriate Response $\left(x^{2}+2\right) d x$ , and We Let $u=x^{2}+2$