A triangle is bounded by the lines y = x, y = -x, and y = 1 When setting up an intergral to find mass or inertia or whatever, why can I not set it up as integral(1, -1) integral(1, x) dydx and instead need to set it up as integral(1, 0) integral(y, -y) dxdy

A triangle is bounded by the lines y = x, y = -x, and y = 1 When setting up an intergral to find mass or inertia or whatever, why can I not set it up as integral(1, -1) integral(1, x) dydx and instead need to set it up as integral(1, 0) integral(y, -y) dxdy

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 17E

See similar textbooks

Related questions

Q: 2. Find the absolute maximum and absolute minimum values off on the given interval. (a)…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 10 S™ f(x) dx 3 If f(x) dx = 3 then 3 10 4f(x

A: given statement is : - ∫310f(x)dx =3 then ∫3104f(x)dx=9then we have to check it is true or…

Q: b) _E=1n"x"

A: The given series is: ∑n=1∞ nnxn

Q: -12-11 -10 -9 -8 -7 -6 -5 -3 -2 -1 4 3 2 4 0 -1 -2 1 2 3 5 What are the vertical asymptote(s) of the…

Q: 11. Consider the graph of the function below. Dashed lines are asymptotes. 34 -2TT -TT y 0 -EIN 2TT…

Q: The population of a bacteria doubles in 30 minutes. How many minutes will it take to make the…

Q: Evaluate 9x 9 (2x - 3)(x + 3) T -dx +C

Q: b) an = Find the limit of the sequence, if it exists. (Again, this is a sequence, not a series)…

A: To find the limit of the sequence, if it exists.an=1-3n5n

Q: The supply for a particular item is given by the function S(x) = 19 + 11x. Find the producer's…

A: formula for producer surplus is =(p)e(x)e-∫abs(x)dxgiven s(x)=19+11x

Q: Solve the system by elimination: 4x - 3y6z = 1 x-y-6z=5 6x - y = -11 Express your answer as an…

Q: A ball is being inflated such that the volume is increasing at a constant rate of 130cm3/s. How fast…

A: Given query is to find rate of change of radius.

Q: An economy has three industries, farming, building, and clothing. For every dollar of food produced,…

Q: The rabbit population at the city park increases by 15% per year. If there are intially 164 rabbits…

Q: For the given cost function C(x) = 40000 + 300x + x² find: a) The cost at the production level 1650…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Inverse Laplace transform of 4 s-4 s²+36 f(t) = 4cos(6t) - F(s)= Select one: O True O False 4 +1000…

Q: The first term of an arithmetic sequence is 11, and the tenth term is 3. (a) Find the common…

Q: Find lim X→∞ lim X→∞ 1 √x 1 √x X dt dt √√₁

A: ∫tndt=tn+1n+1+clet A=limx→∞1x∫1x1tdt

Q: A bakery has the following pricing for large orders of cupcakes. The first 100 cupcakes of any order…

A: A bakery has the following pricing for large orders of cupcakes. The first 100 cupcakes of any order…

Q: 13. Determine which of the following alternating series converge and which diverge. Justify your…

Q: Determine whether the sequence is divergent or Convergent. If it is convergent, evaluate its limit.…

Q: Let f(x, y) = x² - y³ + 12xy. List the critical points: The critical point at the origin is a Select…

Q: Question 9 Evaluate the definite integral 8 (10a + 5) da > Next Question

Q: Determine if the following piecewise defined function is differentiable at x = 0. f(x) lim h→0* 3x -…

A: The given function fx=3x-5,x≥0x2+2x-5,x<0. We have check the function differentiable is…

Q: onsider f(x)=x2+- (a) What value of b makes this f(x) have a local minimum at x = -2? (b) What value…

Q: (3) Find the derivative of the following in terms of x and then find the second derivative. sec(y-x)…

Q: S=4+² -2t³, t = -1

Q: Which equations show an implicit relation between and ? Select all that apply. O X Y y = 3x³ − 2x +…

A: An implicit relation is the one in which the variables x and y cannot be separated to two different…

Q: ے و رو .. + + - + - + 4 T*/

Q: 3 06 02 O The function on the graph above it is not continuous at x = 4 N -2 4 -6 -8

A: NOTE: Refresh your page if you can't see any equations. .

Q: What is the exponential function of the graph shown below? Provide your answer below: f(x) = -9 -10…

A: Graph of the exponential function is given, we have to find its equation.

Q: EXAMPLE 7 Sketch the conic below and find its foci. 25x²9y²-150x + 36y + 414 = 0 SOLUTION We…

Q: Use the relation lim 0-0 lim t→0 sin kt t A. lim t-0 sin 0 0 = 1 to determine the limit. (k…

Q: 17x 9 + 14x5-6x³

A: The given equation is; 17x9+14x5-6x3

Q: " Given what is the outside function f(g(x)) = cos x² and the inside function ? f(x) g(x) so that…

A: Given a composite function

Q: Suppose that f(x) = x² and g(x)= |x|. Then the following composites are both differentiable at x = 0…

Q: Consider a 25-N weight suspended by two wires as shown. If the magnitudes of vectors F₁ and F2 are…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x²yey lim (x,y) → (0, 0) x4…

Q: Find a parametric description of the line segment from the point P to the point Q. P(0,0), Q(8, -20)…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 2i + 4j - 4k, b =…

Q: Convert the equation r = - - 14 sin 0 to Cartesian coordinates. Describe the resulting curve. Choose…

Q: Suppose that 40 students were asked how many courses they were taking this semester. The…

Q: A sleeping bag is on sale for $22.81 and has been discounted 30%. What was the original price of the…

A: NOTE: Refresh your page if you can't see any equations. . the price of the sleeping bag after a 30%…

Q: Find √(526 5x + 3x7) dx + C

Q: If you drive 98 miles and use 7 gallons of gas, what is your rate of gas consumption? miles per…

A: Given query is to find the rate of gas consumption.

Q: 2 4/1 1 (3) Find d dt 1 + t2

Q: Find the inverse of f(x) f ¹(x) = = 52+4 3x − 4

Q: Find the volume of a parallelepiped if four of its eight vertices are. e A(0, 0, 0), B(1, 2, 0),…

A: Given; A(0,0,0), B(1,2,0), C(0,-3,2), D(3,-4,5).

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? Give…

Q: Consider the functions y = (x - 2)² +3. 13. a. Find the inverse of the function. b. Find f-¹(-4). If…

Q: Find the stationary points and local extreme values of f(x, y) = 2x² + xy + 3y² + 4x + y.

A: Extream values

Question

A triangle is bounded by the lines y = x, y = -x, and y = 1

When setting up an intergral to find mass or inertia or whatever, why can I not set it up as

integral(1, -1) integral(1, x) dydx

and instead need to set it up as

integral(1, 0) integral(y, -y) dxdy

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

If o = 2xyz2, vector F = xyi - zj + x²k and C %3D %3D is the curve: x = t2, y = 2t, z = t3 from t = 0 to t = 1 evaluate the following line What is. integrals. i» So dr (i) § Fxdr.
Evelvate F.dv where c - zi and segment y 2K from (-',20) to (3,0,1)
A lamina has mass M = 320 and shape bounded by the z-axis, y-axis and the lines y= 4+3z and r = 7. (a) Enter P, the mass per unit area correct to two decimal places: (b) Enter the Moment of Inertia of the lamina (Mol) about the y-axis correct to two decimal places
Let C be the curve y=(e^1.5x+e^-1.5x)/3 for (0.5,1.7) Find surface area. I'm having a lot of trouble simplifying sqrt(1+ y'^2)
find the center of mass of a thin plate of constant density d covering the given region. The region in the ﬁrst and fourth quadrants enclosed by the curves y = 1/(1 + x^2) and y = -1/(1 + x^2) and by the lines x = 0 and x = 1
Find the center of mass of a thin plate of constant density 8 covering the region bounded by the parabola y = 3x² and the line y = 12. = The center of mass is located at (x, y) (Simplify your answer. Type an ordered pair.)
The 1st quadrant area is bounded by y = x2 + 1, and line y = 5 %3D Find the VOLUME of the solid if this area a) is rotated about Y-axis. Show two solutions by DISKS and by SHELLS with matching answers. Make 2 separate sketches, show the element of volume with its dimensions on each and corresponding differential of volume. b) the same area is rotated about X-axis Make another sketch and use SHELLS ONLY
Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line passing through the point A (1,12) and parallel to the vector u = (1,2). Determine the volume of the passage produced by a complete rotation of S about the x'x axis.