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
What are 3 expressions of 3/4x=15
Over [174]

Answer:

X=20

Step-by-step explanation:

7 0
2 years ago
There are 4grams of fiber in 1/2 cup of oats. how many grams of fiber are in 3 1/2 cuña of oats​
aleksklad [387]

Answer:

28 grams

Step-by-step explanation:

8 x 3 = 24

24 + 4 = 28

7 0
2 years ago
Midpoint (10,4) Endpoint (9,-4), find the coordinates of the other endpoint.​
mestny [16]

Answer:

(11, 12)

Step-by-step explanation:

<u>Mid point coordinates:</u>

  • x = (x₁ + x₂)/2
  • y = (y₁ + y₂)/2

<u>Since midpoint and one endpoint given (10, 4) and (9, -4), the other endpoint:</u>

  • x₂ = 2x - x₁ = 2*10 - 9 = 11
  • y₂ = 2y - y₁ = 2*4 - (-4) = 12

<u>So the other endpoint is: </u>(11, 12)

4 0
3 years ago
Math question can somebody please help me with this math problem
Elodia [21]
You need to add up all the sides of the thing thank you
5 0
3 years ago
Read 2 more answers
Give the digits in the tens place and the hundredths place.
a_sh-v [17]

Answer:

tens:5

hundreths:4

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • The Johnsons own a home whose market value is $93,000. Their municipality taxes at 80% and the rate is 65 mills or $65 per thous
    10·2 answers
  • Need help asap!! please
    5·1 answer
  • 6×2/3-5×0.3+4 what does this equal
    15·2 answers
  • What is -28x + 20x^2?
    10·1 answer
  • Eliana has 40$. she plans to save $25 every week to buy a plane ticket that costs $365. how many weeks will it take her to save
    15·2 answers
  • Solve for m 4=m+4 :) what does m = ?
    10·1 answer
  • Find x, find jl . any help is deeply appreciated :) !​
    13·1 answer
  • Fill in the blank.<br> 5x(2 + 10) = (5x__) + (5 x 10)
    10·2 answers
  • Freddy bought 3 bags of pebbles to put in his fish tank. Each bag contains 295 pebbles. After he put the right amount of pebbles
    7·1 answer
  • There are 240 students in the seventh grade, and 20% are in the Environmental Club. How many students are in the Environmental C
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!