Indefinite Integrals 2
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 (3x-6)^2 dx`Hint
Help VideoCorrect
Correct!
Incorrect
Integration Formula
$$\int x^{\color{#004ec4}{n}} dx=\frac{x^{\color{#004ec4}{n}+1}}{\color{#004ec4}{n}+1}+c$$Sum or Difference Rule
$$ \int (f(x) \pm g(x))dx = \int f(x)dx \pm \int g(x)dx = F(x) \pm G(x) + c $$Formula of Reduced Multiplication (the squared difference)
$$(a-b)^2= a^2-2ab+b^2$$Apply the Formula of Reduced Multiplication to the expression `(3x-6)^2``(3x-6)^2` `=` $$(3x)^2-2\times3x\times6+6^2$$ `=` $$9x^2-36x+36$$ Apply the Sum or Difference Rule$$\int (3x-6)^2dx$$ `=` $$\int(9x^2-36x+36)dx$$ `=` $$\int 9x^2dx-\int 36xdx+\int 36dx $$ Find the Indefinite Integral$$\int 9x^2dx-\int 36xdx+\int 36dx $$ Take the constants out of the integral signs `=` $$9\int x^2dx-36\int xdx+36\int 1dx $$ `=` $$9\int x^\color{#004ec4}{2}dx-36\int x^\color{#004ec4}{1}dx+36\int x^\color{#004ec4}{0}dx $$ `=` $$9\frac{x^{\color{#004ec4}{2}+1}}{\color{#004ec4}{2}+1}-36\frac{x^{\color{#004ec4}{1}+1}}{\color{#004ec4}{1}+1}+36\frac{x^{\color{#004ec4}{0}+1}}{\color{#004ec4}{0}+1}+c$$ Apply the Integration Formula `=` $$9\frac{x^{3}}{3}-36\frac{x^{2}}{2}+36\frac{x^{1}}{1}+c$$ `=` $$3x^{3}-18x^{2}+36x+c$$ `3x^{3}-18x^{2}+36x+c` -
Question 2 of 5
2. Question
Integrate`int sqrt(3x-5) dx`Hint
Help VideoCorrect
Well Done!
Incorrect
Integration Formula
$$\int f(x)^{\color{#004ec4}{n}} dx=\frac{f(x)^{\color{#004ec4}{n}+1}}{(\color{#004ec4}{n}+1)f'(x)}+c$$`int sqrt{3x-5} dx ` can be written as `int (3x-5)^{1/2}dx`Find the Indefinite Integral$$\int{(3x-5)}^{\color{#004ec4}{\frac{1}{2}}}dx$$ `=` $$\frac{(3x-5)^{\color{#004ec4}{\frac{1}{2}}+1}}{(\color{#004ec4}{\frac{1}{2}}+1)(3x-5)’}+c$$ Apply the Integration Formula `=` $$\frac{(3x-5)^{\color{#004ec4}{\frac{3}{2}}}}{\color{#004ec4}{\frac{3}{2}}\times 3}+c$$ `=` `2/9 (3x-5)^{3/2}+c` `=` `2/9 sqrt{(3x-5)^3}+c` `{2sqrt{(3x-5)^3}}/9 + c` -
Question 3 of 5
3. Question
Integrate$$\int\frac{6}{\sqrt[3]{x}}dx$$Hint
Help VideoCorrect
Excellent!
Incorrect
Integration Formula
$$\int x^{\color{#004ec4}{n}} dx=\frac{x^{\color{#004ec4}{n}+1}}{\color{#004ec4}{n}+1}+c$$Find the Indefinite Integral$$\int\frac{6}{\sqrt[3]{x}}dx$$ `=` $$6\int\frac{1}{\sqrt[3]{x}}dx$$ Take the constant `6` out of the integral sign `=` $$6\int x^{\color{#004ec4}{-\frac{1}{3}}}dx$$ The integral can be written `=` $$6\frac{x^{\color{#004ec4}{-\frac{1}{3}}+1}}{\color{#004ec4}{-\frac{1}{3}}+1}+c$$ Apply the Integration Formula `=` $$ 6\frac{x^{\color{#004ec4}{\frac{2}{3}}}}{\color{#004ec4}{\frac{2}{3}}}+c$$ `=` $$\frac{18}{2} x^{ \frac{2}{3} }+c$$ `=` `9x^{2/3} + c` `9x^{2/3} + c` -
Question 4 of 5
4. Question
Integrate$$\int\sqrt[3]{4x+3}$$Hint
Help VideoCorrect
Fantastic!
Incorrect
Integration Formula
$$\int f(x)^{\color{#004ec4}{n}} dx=\frac{f(x)^{\color{#004ec4}{n}+1}}{(\color{#004ec4}{n}+1)f'(x)}+c$$$$\int\sqrt[3]{4x+3} dx $$ can be written as $$\int(4x+3)^{\frac{1}{3}}dx$$Find the Indefinite Integral$$\int{(4x+3)}^{\color{#004ec4}{\frac{1}{3}}}dx$$ `=` $$\frac{(4x+3)^{\color{#004ec4}{\frac{1}{3}}+1}}{(\color{#004ec4}{\frac{1}{3}}+1)(4x+3)’}+c$$ Apply the Integration Formula `=` $$\frac{(4x+3)^{\color{#004ec4}{\frac{4}{3}}}}{\color{#004ec4}{\frac{4}{3}}\times 4}+c$$ `=` $$\frac{(4x+3)^{{\frac{4}{3}}}}{{\frac{16}{3}}}+c$$ `=` $$\frac{3}{16}(4x+3)^{\frac{4}{3}}+c$$ `3/16 (4x+3)^{4/3}+c` -
Question 5 of 5
5. Question
Integrate`int 1/{3(4x-5)^3} dx`Hint
Help VideoCorrect
Nice Job!
Incorrect
Integration Formula
$$\int f(x)^{\color{#004ec4}{n}} dx=\frac{f(x)^{\color{#004ec4}{n}+1}}{(\color{#004ec4}{n}+1)f'(x)}+c$$`int 1/{3(4x-5)^3}dx` can be written as `int 1/3 (4x-5)^{-3}dx`Find the Indefinite Integral$$\int\frac{1}{3}(4x-5)^{\color{#004ec4}{-3}}dx$$ `=` $$\frac{1}{3}\int(4x-5)^{\color{#004ec4}{-3}}dx$$ Take the constant `1/3` out of the integral sign `=` $$\frac{1}{3}\frac{(4x-5)^{\color{#004ec4}{-3}+1}}{(\color{#004ec4}{-3}+1)(4x-5)’}+c$$ Apply the Integration Formula `=` $$\frac{1}{3}\frac{(4x-5)^{\color{#004ec4}{-2}}}{\color{#004ec4}{-2}\times 4}+c$$ `=` $$\frac{1}{3}(-\frac{1}{8})(4x-5)^{-2}+c$$ `=` $$-\frac{1}{24}(4x-5)^{-2}+c$$ Simplify `=` $$-\frac{1}{24(4x-5)^2}+c$$ Apply Negative Indice law $$-\frac{1}{24(4x-5)^2}+c$$
Quizzes
- Indefinite Integrals 1
- Indefinite Integrals 2
- Indefinite Integrals 3
- Definite Integrals
- Areas Between Curves and the Axis 1
- Areas Between Curves and the Axis 2
- The Area Between Curves
- Volumes of Revolution 1
- Volumes of Revolution 2
- Volumes of Revolution 3
- Trapezoidal Rule
- Simpsons Rule
- Integral of a Trigonometric Function 1
- Integral of a Trigonometric Function 2
- Applications of Integration for Trig Functions