Indefinite Integrals 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
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
- Answered
- Review
-
Question 1 of 5
1. Question
Integrate`int x^3 dx`Hint
Help VideoCorrect
Nice Job!
Incorrect
Integration Formula
$$\int x^{\color{#004ec4}{n}} dx=\frac{x^{\color{#004ec4}{n}+1}}{\color{#004ec4}{n}+1}+c$$Find the Indefinite Integral$$\int x^{\color{#004ec4}{3}} dx$$ `=` $$\frac{x^{\color{#004ec4}{3}+1}}{\color{#004ec4}{3}+1}+c$$ Apply the standard formula `=` `(x^(4))/(4) +c` `(x^(4))/(4) +c ` -
Question 2 of 5
2. Question
Integrate`int (5-2x-x^2)dx`Hint
Help VideoCorrect
Excellent!
Incorrect
Integration Formula
$$\int x^{\color{#004ec4}{n}} dx=\frac{x^{\color{#004ec4}{n}+1}}{\color{#004ec4}{n}+1}+c$$Sum or Difference Rule
$$ \int (f(x) \pm g(x))dx = \int f(x)dx \pm \int g(x)dx = F(x) \pm G(x) + c $$Apply the Sum or Difference Rule`int (5-2x-x^2) dx` `=` `int 5 dx-int 2x dx-int x^2 dx` Find the Indefinite Integral`int5dx-int2xdx-intx^2dx` `=` $$\int5x^{\color{#004ec4}{0}}dx-\int2x^{\color{#004ec4}{1}}dx-\int x^{\color{#004ec4}{2}}dx$$ Take the constants out of the integral signs `=` $$5\int x^{\color{#004ec4}{0}}dx-2\int x^{\color{#004ec4}{1}}dx-\int x^{\color{#004ec4}{2}}dx$$ `=` $$5\frac{x^{\color{#004ec4}{0}+1}}{\color{#004ec4}{0}+1}-2\frac{x^{\color{#004ec4}{1}+1}}{\color{#004ec4}{1}+1}-\frac{x^{\color{#004ec4}{2}+1}}{\color{#004ec4}{2}+1}+c$$ Use the Integration Formula `=` `5x^1/1-2x^2/2-x^3/3+c` `=` `5x-x^2-x^3/3+c` `5x-x^2-x^3/3+c` -
Question 3 of 5
3. Question
Integrate`int(1-2x)^6dx`Hint
Help VideoCorrect
Correct!
Incorrect
Integration Formula
$$\int f(x)^{\color{#004ec4}{n}} dx=\frac{f(x)^{\color{#004ec4}{n}+1}}{(\color{#004ec4}{n}+1)f'(x)}+c$$Find the Indefinite Integral$$\int (1-2x)^{\color{#004ec4}{6}}dx$$ `=` $$\frac{(1-2x)^{\color{#004ec4}{6}+1}}{(\color{#004ec4}{6}+1)(1-2x)’}+c$$ Apply the Integration Formula `=` $$\frac{(1-2x)^{\color{#004ec4}{7}}}{\color{#004ec4}{7}\times(-2)}+c$$ `=` `-1/14 (1-2x)^7+c` `-1/14 (1-2x)^7+c` -
Question 4 of 5
4. Question
Integrate`int(5x-4)^5dx`Hint
Help VideoCorrect
Great Work!
Incorrect
Integration Formula
$$\int f(x)^{\color{#004ec4}{n}} dx=\frac{f(x)^{\color{#004ec4}{n}+1}}{(\color{#004ec4}{n}+1)f'(x)}+c$$Find the Indefinite Integral$$\int (5x-4)^{\color{#004ec4}{5}}dx$$ `=` $$\frac{(5x-4)^{\color{#004ec4}{5}+1}}{(\color{#004ec4}{5}+1)(5x-4)’}+c$$ Apply the Integration Formula `=` $$\frac{(5x-4)^{\color{#004ec4}{6}}}{\color{#004ec4}{6}\times 5}+c$$ `=` `1/30 (5x-4)^6+c` `1/30 (5x-4)^6+c` -
Question 5 of 5
5. Question
Integrate`int sqrt{x}(1+1/sqrt{x})dx`Hint
Help VideoCorrect
Great Work!
Incorrect
Integration Formula
$$\int x^{\color{#004ec4}{n}} dx=\frac{x^{\color{#004ec4}{n}+1}}{\color{#004ec4}{n}+1}+c$$Sum or Difference Rule
$$ \int (f(x) \pm g(x))dx = \int f(x)dx \pm \int g(x)dx = F(x) \pm G(x) + c $$`sqrt{x}(1+1/sqrt{x})` can be written as$$\color{#004ec4}{\sqrt{x}}(1+\frac{1}{\sqrt{x}})$$ `=` $$\color{#004ec4}{\sqrt{x}}\times 1+\color{#004ec4}{\sqrt{x}}\times\frac{1}{\sqrt{x}}$$ `=` $$\sqrt{x}+1$$ Apply the Sum or Difference Rule$$\int\sqrt{x}(1+\frac{1}{\sqrt{x}})dx$$ `=` $$\int(\sqrt{x}+1)dx$$ `=` $$\int\sqrt{x}dx +\int 1dx$$ Find the Indefinite Integral$$\int\sqrt{x}dx +\int 1dx$$ `=` $$\int x^\color{#004ec4}{\frac{1}{2}}dx +\int 1x^\color{#004ec4}{0}dx$$ An alternative way to write the equation `=` $$\frac{x^{\color{#004ec4}{\frac{1}{2}}+1}}{\color{#004ec4}{\frac{1}{2}}+1}+\frac{x^{\color{#004ec4}{0}+1}}{\color{#004ec4}{0}+1}+c$$ Apply the Integration Formula `=` $$\frac{x^{\frac{3}{2}}}{\frac{3}{2}}+\frac{x^{1}}{1}+c$$ `=` $$\frac{2}{3}\sqrt{x^3}+x+c$$ `2/3 sqrt{x^3}+x+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