Topics
>
Calculus and Integration>
Integration>
Indefinite Integrals of Exponential Functions>
Indefinite Integrals of Exponential FunctionsIndefinite Integrals of Exponential Functions
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 6 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- Answered
- Review
-
Question 1 of 6
1. Question
Find the integral$$\int e^{4x} dx$$Hint
Help VideoCorrect
Great Work!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int e^{\color{#004ec4}{4}x} dx$$ `=` $$\frac{1}{\color{#004ec4}{4}} e^{\color{#004ec4}{4}x} +c$$ Substitute known values `1/4 e^(4x)+c` -
Question 2 of 6
2. Question
Find the integral$$\int e^{\frac{1}{2}x} dx$$Hint
Help VideoCorrect
Correct!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int e^{\color{#004ec4}{\frac{1}{2}}x} dx$$ `=` $$\frac{1}{\color{#004ec4}{\frac{1}{2}}} e^{\color{#004ec4}{\frac{1}{2}}x} +c$$ Substitute known values `=` `2e^(1/2x) +c` Reciprocate the denominator `2e^(1/2x) +c` -
Question 3 of 6
3. Question
Find the integral$$\int 12e^{3x} dx$$Hint
Help VideoCorrect
Keep Going!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int 12e^{\color{#004ec4}{3}x} dx$$ `=` $$\frac{12}{\color{#004ec4}{3}} e^{\color{#004ec4}{3}x} +c$$ Substitute known values `=` `4e^(3x)+c` Simplify `4e^(3x)+c` -
Question 4 of 6
4. Question
Find the integral$$\int e^{2x-5} dx$$Hint
Help VideoCorrect
Fantastic!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int e^{\color{#004ec4}{2}x-5} dx$$ `=` $$\frac{1}{\color{#004ec4}{2}} e^{\color{#004ec4}{2}x-5} +c$$ Substitute known values `1/2 e^(2x-5) +c` -
Question 5 of 6
5. Question
Find the integral$$\int 6e^{3x+4} dx$$Hint
Help VideoCorrect
Excellent!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int 6e^{\color{#004ec4}{3}x+4} dx$$ `=` $$\frac{6}{\color{#004ec4}{3}} e^{\color{#004ec4}{3}x+4} +c$$ Substitute known values `=` `2e^(3x+4)+c` Simplify `2e^(3x+4)+c` -
Question 6 of 6
6. Question
Find the integral$$\int \frac{1}{2} e^{5-3x} dx$$Hint
Help VideoCorrect
Nice Job!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int \frac{1}{2}e^{5-\color{#004ec4}{3}x} dx$$ `=` $$\frac{\frac{1}{2}}{\color{#004ec4}{-3}} e^{5-\color{#004ec4}{3}x} +c$$ Substitute known values `=` `-1/6 e^(5-3x)+c` Simplify `-1/6 e^(5-3x)+c`
Quizzes
- Indefinite Integrals 1
- Indefinite Integrals 2
- Indefinite Integrals 3
- Indefinite Integrals of Exponential Functions
- Indefinite Integrals of Logarithmic Functions 1
- Indefinite Integrals of Logarithmic Functions 2
- Indefinite Integrals of Trig Functions
- Definite Integrals
- Definite Integrals of Exponential Functions
- Definite Integrals of Logarithmic Functions
- Definite Integrals of Trig Functions
- Areas Between Curves and the Axis 1
- Areas Between Curves and the Axis 2
- Area Between Curves
- Volumes of Revolution 1
- Volumes of Revolution 2
- Volumes of Revolution 3
- Trapezoidal Rule
- Simpsons Rule
- Applications of Integration for Trig Functions