Find the area of the region bounded by the graphs of the given functions x=3y²−9 x=0 y=0 y=1



Answer to a math question Find the area of the region bounded by the graphs of the given functions x=3y²−9 x=0 y=0 y=1

Expert avatar
60 Answers
To find the area of the region bounded by the given functions, we need to first find the points of intersection.

Setting the two given functions equal to each other:

3y^2 - 9 = 0

y^2 = 3

y = \pm \sqrt{3}

So, the points of intersection are at (0,0) and at \left(\pm \sqrt{3}, \frac{1}{2}\right) .

Since we are interested in the area between x=3y^2-9 and x=0 , we need to integrate the difference of their equations with respect to y from y=0 to y=1 .

A = \int_{0}^{1} \left(3y^2-9-0\right) \,dy

A = \int_{0}^{1} (3y^2-9) \, dy

A = \left[y^3-9y\right]_{0}^{1}

A = \left(1^3-9(1)\right) - \left(0^3-9(0)\right)

A = 1-9 = -8

Therefore, the area of the region bounded by the graphs of the given functions is \boxed{8 sq. units} .

Frequently asked questions (FAQs)
What is the sine of 45 degrees?
What is the common base for the logarithmic function f(x) = log x and the natural logarithmic function f(x) = ln x?
What is 0.45 as a percentage?
New questions in Mathematics
The gross domestic product the gdp for the United States in 2017 was approximately $2.05x10^3. If you wrote this number in standard notation , it would be 205 followed by how many zeros
the value of sin 178°58'
To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:
Find the derivatives for y=X+1/X-1
What is the total tolerance for a dimension from 1.996" to 2.026*?
Determine the general equation of the straight line that passes through the point P (2;-3) and is parallel to the straight line with the equation 5x – 2y 1 = 0:
The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?
20% of 3500
Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.
We have two distributions: A (M = 66.7, 95% CI = [60.3, 67.1]) / B (M = 71.3 95% CI = [67.7, 74.9]). Erin maintains that B is significantly larger than A. Provide your opinion on Erin’s argument and justify your opinion.
We plan to test whether the mean mRNA expression level differs between two strains of yeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n samples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene, using an unpaired two-sample t-test for each gene (the particular type of test does not matter). a) What are the null hypotheses in these tests (in words)? [2] b) If, in fact, the two strains are identical, how many of these tests do we expect to produce a P-value exceeding 1/4? [2]
A given initial capital in simple interest at the annual rate and for 27 months produced the accumulated capital of 6600 um if the same capital had been invested at the same rate but during 28 months the said accumulated capital would be increased in an amount corresponding to 0.75% of the initial capital Calculate the initial capital and the annual rate at which it was invested
Write the inequality in the form of a<x<b. |x| < c^2
Solve the following system of equations using substitution. y=-4x- 11. 3x+7y=-2
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?