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
Mandarinka [93]
3 years ago
14

Calculus I integral problem

Mathematics
1 answer:
mina [271]3 years ago
7 0

Answer:  -\frac{\sqrt{35}}{2}

In terms of typing this in on a keyboard, you could say -sqrt(35)/2

===================================================

Work Shown:

We'll use u-substitution here

Let u = x^2, so du/dx = 2x which rearranges to du = 2x*dx and we can say xdx = du/2

Because we are changing from x^2 to u, this means we need to change the limits of integration

If x = -2, then u = x^2 = (-2)^2 = 4

If x = 0, then u = x^2 = 0^2 = 0

Despite 4 being larger than 0, we still place 4 at the bottom limit and we'll just swap them later.

This means we have the following steps

\displaystyle \int_{-2}^{0}xg(x^2)\sqrt{7}dx\\\\\\\displaystyle \sqrt{7}\int_{-2}^{0}xg(x^2)dx\\\\\\\displaystyle \sqrt{7}\int_{-2}^{0}g(x^2)xdx\\\\\\\displaystyle \sqrt{7}\int_{4}^{0}g(u)\frac{du}{2}\\\\\\\displaystyle -\sqrt{7}\int_{0}^{4}g(u)\frac{du}{2}\\\\\\\displaystyle -\sqrt{7}*\frac{1}{2}\int_{0}^{4}g(u)du\\\\\\\displaystyle -\frac{\sqrt{7}}{2}\sqrt{5}\\\\\\\displaystyle -\frac{\sqrt{7}*\sqrt{5}}{2}\\\\\\\displaystyle -\frac{\sqrt{7*5}}{2}\\\\\\\displaystyle -\frac{\sqrt{35}}{2}\\\\\\

Notice when I swapped the limits of integration (4 and 0 to 0 and 4) I placed a negative sign out front.

The rule is \displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx

You might be interested in
Please give me an answer
adoni [48]
Express 0.31 as a fraction and express 0.2 as a fraction
4 0
3 years ago
Read 2 more answers
Decide if each pair of lines is parallel, perpendicular, or neither.
MA_775_DIABLO [31]

Answer:

Hi

Step-by-step explanation:

I feel like this question is hard to say but I will try my best. 1st one is pparallel, 2 is perpendicular, 3 is perpendicular and 4 is parallel.

#Im only in 15th grade

4 0
2 years ago
A pair of basketball shoes was originally priced at 80. It was marked up by 37.5% what was the retail price of the shoes
OlgaM077 [116]

Answer:

67

Step-by-step explanation:

4 0
3 years ago
A small boat can travel at 28 per hour how many hours will it take to go across the bay that is 56 miles wide
dsp73

Answer:

2 hours

Remember that time = distance/rate

The distance you need to cover is 56 miles, while you go 28 miles per hour. Using these, we get this:

time=56/28

time=2

So it will take two hours to go across a 56 mile wide bay at 28 mph.

Step-by-step explanation:

8 0
3 years ago
The height of a house is 39.2 ft, a doll house replica is 2.8 ft. What is the scale<br> factor?
Tatiana [17]
I might be wrong cause I don’t removed this from 4 years ago but it should be 36.4 also plz mark brainlyiest
3 0
2 years ago
Other questions:
  • My number has 2 digits and is even, the sum of my numbers digits is 10, the difference of the two digits of my number is 6, my n
    10·1 answer
  • Which inequality represents the graph below
    10·1 answer
  • The manager of music is giving away 255 music downloads at its grand opening event.
    5·1 answer
  • Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B123%7D%7B65%7D" id="TexFormula1" title="\frac{123}{65}" alt="\frac{123}{65}"
    14·1 answer
  • Joey used
    12·1 answer
  • Help me i need to get a good grade on this testtt
    5·2 answers
  • The students at Walden Middle School are selling tins of popcorn to raise money for new uniforms. They sold 42 tins in the first
    10·2 answers
  • Pls help me i will make u a brainest
    8·1 answer
  • Given vector u = (3, 1) and v = (2,-4), determine the value of v – 4u in<br> component form.
    5·1 answer
  • Jackson’s rectangular bedroom has an area of 90 square feet. The area of his bedroom is 9 times that of his rectangular closet.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!