Mathematics, 12.07.2019 05:50 bellapearl163
Find the volume of the solid that lies under the hyperbolic paraboloid z = 4 + x 2 − y 2 and and above the square r = [−1, 1] × [0, 2].
Answers: 1
and above the square r = [−1, 1] × [0, 2] is 
and the surface 
The planes 
and 
The planes 
and 
![\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)\\\\=\displaystyle \int\limit_0^2\,dx \left[4y+x^2y-\dfrac{y^3}{3} \right]_{-1}^1\\\\=\displaystyle \int\limit_0^2\,dx \left[ \left(4(1)+x^2(1)-\dfrac{(1)^3}{3} \right)- \left(4(-1)+x^2(-1)-\dfrac{(-1)^3}{3} \right)\right]\\\\=\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\](/tpl/images/0079/8541/6cca0.png)
![\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\=\left[\dfrac{22}{3}x+\dfrac{2x^3}{3}\right]_0^2\\\\=\left(\dfrac{22}{3}(2)+\dfrac{2(2)^3}{3}\right) - \left(\dfrac{22}{3}(0)+\dfrac{2(0)^3}{3}\right)\\\\=20 \text{ cubic units}](/tpl/images/0079/8541/d1024.png)
Another question on Mathematics
Mathematics, 21.06.2019 16:30
What is the area of a pizza with a radius of 40 cm leave the answer in terms of π to find your exact answer 40π cm² 1600π cm² 800π cm² 80π cm² π=pi
Answers: 1
Mathematics, 21.06.2019 18:50
Need 50 will mark brainliest answer. find the lengths of all the sides and the measures of the angles.
Answers: 1
Mathematics, 21.06.2019 23:00
John has 1/2 pound of oranges to share with julie. if they share the oranges equally, how much will each of them have?
Answers: 1
Mathematics, 22.06.2019 02:10
The human resources manager at a company records the length, in hours, of one shift at work, x. he creates the probability distribution below. what is the probability that a worker chosen at random works at least 8 hours? 0.62 0.78 0.84 0.96
Answers: 2
You know the right answer?
Find the volume of the solid that lies under the hyperbolic paraboloid z = 4 + x 2 − y 2 and and abo...
Questions
Biology, 04.02.2021 22:30
SAT, 04.02.2021 22:30
History, 04.02.2021 22:30
Social Studies, 04.02.2021 22:30
Mathematics, 04.02.2021 22:30
Mathematics, 04.02.2021 22:30
Mathematics, 04.02.2021 22:40
Mathematics, 04.02.2021 22:40
Mathematics, 04.02.2021 22:40
English, 04.02.2021 22:40
Mathematics, 04.02.2021 22:40
Mathematics, 04.02.2021 22:40
