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
Genrish500 [490]
4 years ago
15

Evaluate the double integral ∬d(x2+6y)da, where d is bounded by y=x, y=x3, and x≥0. answer: -0.6548

Mathematics
1 answer:
JulijaS [17]4 years ago
3 0
We want to evaluate
\int \int (x^{2}+6y)dA
over the region bounded by
y = x, y = x³, and x ≥ 0.

The intersection of the curves y=x and y = x³ is determined as
x³ = x
x(x² - 1) = 0
x(x + 1)(x - 1) = 0
x =0, x = -1, x = 1.
Because x ≥ 0, the intersection points are
(0,0) and (1,1)

The region for the integration is shown shaded in the graph shown below.

Let
y₁ = x³, the curve.
y₂ = x, the straight line
Then the integral may be written as
\int_{0}^{1} dx \int_{y1}^{y2} (x^{2}+6y)dy \\\\ = \int _{0}^{1}dx \int_{x^3} ^{x} (x^{2}+6y)dy \\

The inner integral yields
[x^{2}y+3y^{2}]_{x^{3}}^{x} = x^{3} - x^{5} + 3(x^{2} - x^{6})

The outer integral yields
\int_{0}^{1} (x^{3}-x^{5}+3x^{2}-3x^{6})dx \\\\ = [ \frac{x^{4}}{4} - \frac{x^{6}}{6} +3 (\frac{x^{3}}{3}) -3( \frac{x^{7}}{7})]_{0}^{1} \\\\ =   \frac{55}{84}

Answer: 55/84 (or 0.655)

You might be interested in
Answer all 10 and I will give you brainliest
navik [9.2K]

Answer:

c,b,a

Step-by-step explanation:

8 0
3 years ago
Hey! Does can anyone help me with this? Thank you!
maw [93]

Answer:

=x^3/4

Step-by-step explanation:

(x^1/2)(x^1/4)

same base

1/2+1/4

=3/4

=x^3/4

4 0
2 years ago
5. Five people are standing in a line. Brittany is
choli [55]

Answer:

Devin.

Step-by-step explanation:

The order in line would be Callie, Ana, Devin, Brittany, Evan.

3 0
4 years ago
If josie missed 8 questions how many of them did she get correct
AleksandrR [38]

Answer:

Step-by-step explanation:

how many questions was it out of ?

but you must take away the 8 for the total amount of questions

7 0
3 years ago
Is the difference of two positive rational number always positive
salantis [7]
No, it's not always positive. If the first rational number is smaller than the second one in a substraction, then the result will be negative. For example:

0.2 - 0.5 = -0.3
5 - 5.1 = -0.1
4 0
4 years ago
Read 2 more answers
Other questions:
  • Nine less than four times a number equals fifteen
    12·2 answers
  • Fill in the blank please.
    10·1 answer
  • The formula κ​(x)= f′′(x) 1+f′(x)23/2 expresses the curvature of a​ twice-differentiable plane curve as a function of x. Use thi
    8·1 answer
  • Describe the transformation done to y = 1/x to get y = 1/4x -12?
    5·1 answer
  • For the breakfast buffet, Mr. Walker must equally divide 12 loaves of bread between seven platters. How many loaves of bread are
    15·1 answer
  • Simplify h(w)=6*2^(w-1)<br><br>Answer:<br>㏒₂(hw/6)=w-1
    14·1 answer
  • The endpoints of segment GH are G(-5,5) and H(8, 19). What is the midpoint of<br> segment GH?
    6·1 answer
  • In which equation is the constant of proportionality 5?
    14·1 answer
  • at time t, the position of a body moving along the s-axis is s=t^3 - 12t^2 + 36t m. Find the total distance traveled by the body
    12·1 answer
  • Prove that 4^2n + 10n − 1 is divisible by 25. [hint: binomial theorem]​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!