Which of the following statements match the indefinite integral S(3ª) dx? 3² ○ (3²) dx = 3 +C In Of(3²) dx = = 3² In 3 +C ○ (3²) dx = 3ª + C Of(3²) dx = 3 +C
Which of the following statements match the indefinite integral S(3ª) dx? 3² ○ (3²) dx = 3 +C In Of(3²) dx = = 3² In 3 +C ○ (3²) dx = 3ª + C Of(3²) dx = 3 +C
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Integral Practice Problem
**Question:** Which of the following statements match the indefinite integral \( \int \left(3^x\right) \, dx \)?
#### Options:
1. \( \int \left(3^x\right) \, dx = \dfrac{3^x}{\ln 3} + C \)
2. \( \int \left(3^x\right) \, dx = -\dfrac{3^x}{\ln 3} + C \)
3. \( \int \left(3^x\right) \, dx = 3^x + C \)
4. \( \int \left(3^x\right) \, dx = \dfrac{3^x}{3} + C \)
**Explanation:**
When integrating an exponential function \(a^x\), the formula used is:
\[
\int a^x \, dx = \dfrac{a^x}{\ln a} + C
\]
For the given problem, where \(a = 3\), the integral becomes:
\[
\int 3^x \, dx = \dfrac{3^x}{\ln 3} + C
\]
Thus, the correct statement is:
\[
\int \left(3^x\right) \, dx = \dfrac{3^x}{\ln 3} + C
\]
**Answer:** The first option is correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b1d198d-95a1-4d0b-9915-fffff0f3c2fd%2F4de6cd70-1512-438a-a08e-d15990bc10ad%2Fg1es4w_processed.png&w=3840&q=75)
Transcribed Image Text:### Integral Practice Problem
**Question:** Which of the following statements match the indefinite integral \( \int \left(3^x\right) \, dx \)?
#### Options:
1. \( \int \left(3^x\right) \, dx = \dfrac{3^x}{\ln 3} + C \)
2. \( \int \left(3^x\right) \, dx = -\dfrac{3^x}{\ln 3} + C \)
3. \( \int \left(3^x\right) \, dx = 3^x + C \)
4. \( \int \left(3^x\right) \, dx = \dfrac{3^x}{3} + C \)
**Explanation:**
When integrating an exponential function \(a^x\), the formula used is:
\[
\int a^x \, dx = \dfrac{a^x}{\ln a} + C
\]
For the given problem, where \(a = 3\), the integral becomes:
\[
\int 3^x \, dx = \dfrac{3^x}{\ln 3} + C
\]
Thus, the correct statement is:
\[
\int \left(3^x\right) \, dx = \dfrac{3^x}{\ln 3} + C
\]
**Answer:** The first option is correct.
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