question 2 (1 point)\nthe substitution ( u = 3x ) transforms the integral ( int e^{3x}dx ) into\n( \bigcirc…

question 2 (1 point)\nthe substitution ( u = 3x ) transforms the integral ( int e^{3x}dx ) into\n( \bigcirc int \frac{1}{9}e^{u}du )\n( \bigcirc int \frac{1}{3}e^{u}du )\n( \bigcirc int e^{3u}du )\n( \bigcirc int \frac{1}{3}e^{3u}du )\n( \bigcirc int e^{u}du )

question 2 (1 point)\nthe substitution ( u = 3x ) transforms the integral ( int e^{3x}dx ) into\n( \bigcirc int \frac{1}{9}e^{u}du )\n( \bigcirc int \frac{1}{3}e^{u}du )\n( \bigcirc int e^{3u}du )\n( \bigcirc int \frac{1}{3}e^{3u}du )\n( \bigcirc int e^{u}du )

Answer

Explanation:

Step1: Differentiate (u = 3x)

If (u = 3x), then (du=3dx), and (dx=\frac{1}{3}du).

Step2: Substitute (u) and (dx) into the integral

The original integral (\int e^{3x}dx) becomes (\int e^{u}\cdot\frac{1}{3}du=\int\frac{1}{3}e^{u}du)

Answer:

(\int\frac{1}{3}e^{u}du) (the second option)