1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sineoko [7]
2 years ago
11

Calculate the total area of the shaded region.

Mathematics
1 answer:
LUCKY_DIMON [66]2 years ago
7 0

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

You might be interested in
A computer that originally cost $850 is on sale for 15%off. What is the sale price of the computer show your work
Yakvenalex [24]
If it is on sale for 15%, then you are paying 85% (100-15) of the original price.

To find 85% of 850, you do 850*.85 to get $722.50

Hope this helps
4 0
3 years ago
Read 2 more answers
30% of students at Greenville High School participate in a sport. There are 540 students in the school. How many students in the
ivanzaharov [21]

Answer:

162 student play sports

Step-by-step explanation:

.3 represents 30 precent, so multiply 540 by .3 to get your awnser this is because the .3 is less than one so the multiplying will not raise the number but lower it to 162

6 0
2 years ago
How you do this need help​
Elina [12.6K]
7.5 hours total divided by .5 hours per arrangement would be 15 arrangements.
7 0
3 years ago
1. What is the range of the data?
stira [4]
Answers:

1.) 78 would be the range

3.) 18.8 or letter C would be correct

4.) 9.4
6 0
2 years ago
What is 1/20 as a decimal
Alexandra [31]

Your answer would be 0.05

7 0
2 years ago
Other questions:
  • A massage costs $81.50 per hour. How much will a massage for 2.5 hours cost? $
    7·1 answer
  • Can someone please help me imma die :((((
    14·2 answers
  • What is -2(× - 4) in distributive property
    9·1 answer
  • Solve for z in a=x+z
    13·1 answer
  • 2/3b + 5 = 20 - b whats the answer here?
    7·1 answer
  • Hi I would really appreciate some help fast! This is 8th grade scatter plot question
    7·1 answer
  • X = 4y + 3, 2x + y = -3<br> System of Equations
    13·1 answer
  • Find the length of the rectangle.
    7·2 answers
  • 3x+y=23, 6x-y=50, what is the value of x and y
    9·1 answer
  • Help with number 1 pls
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!