Who are the experts?Our certified Educators are genuine professors, teachers, and also scholars who use their scholastic expertise to tackle your toughest questions. Educators go v a rigorous application process, and also every answer they send is the evaluation by ours in-house editorial team.

You are watching: Find the area of the region bounded by the graphs of the equations


*

We are asked to uncover the area that the an ar bounded through `f(x)=-x^2+4x` and also `y=0` .

We can element the quadratic come y=-x(x-4); the x-intercepts space 0 and 4.

The equivalent question then is to discover the identify integral `int_0^4 (-x^2+4x)dx` .

`int_0^4 (-x^2+4x)dx=-x^3/3+2x^2 |_0^4`

`=(-64/3+32)-(0+0)=32/3 `

for this reason the area...


Start your 48-hour complimentary trial come unlock this answer and also thousands more. Enjoy juniorg8.com ad-free and cancel anytime.


We room asked to discover the area the the an ar bounded through `f(x)=-x^2+4x` and `y=0` .

We can aspect the quadratic come y=-x(x-4); the x-intercepts are 0 and 4.

The identical question then is to find the definite integral `int_0^4 (-x^2+4x)dx` .

`int_0^4 (-x^2+4x)dx=-x^3/3+2x^2 |_0^4`

`=(-64/3+32)-(0+0)=32/3 `

So the area bounded by the offered curve and also the x-axis is 32/3.

See more: A Relationship Can Be Damaged By, Can A Damaged Relationship Be Repaired

An different approach is to use a Riemann sum:

The area can be uncovered by `lim_n->oo sum_i=1^n f(c_i)Delta x_i`

If we use a constant partition and also choose the right-hand endpoint in each subinterval us get:

`A=lim_n->oo sum_i=1^n (-((4i)/n)^2+4((4i)/n))(4/n) `

`=lim_n->oo<(-64)/(n^2)sum_i=1^n(i^2/n-i)> `

`=lim_n->oo<(-64)/n^2(1/n((n(n+1)(2n+1))/6)-(n(n+1))/2)> `

`=lim_n->oo<(-64)/n^2(1/3n^2+1/2n+1/3-n^2/2-n/2)> `

`=lim_n->oo<(-64)/3-(32)/n-(64)/n^3+32+(32)/n> `

`=(-64)/3+32=32/3=10.bar(6) `

The graph:


approved by juniorg8.com Editorial Team

Ask a Question

asking a question
Submit question

Popular Questions


check out all

Related Questions

Browse all
Math

latest answer posted September 09, 2016 in ~ 2:21:21 to be


`y = x, y = 4, x =0` uncover a such the the heat x = a divides the region bounded through the graphs of the equations into two areas of same area.


1 education answer

Math

latest answer post September 13, 2016 in ~ 10:41:06 pm


`y^2 = 4-x , x = 0` discover a such the the heat x = a divides the region bounded by the graphs the the equations into two regions of equal area.


3 educator answers

Math

latest answer post September 13, 2016 at 10:28:41 afternoon


`y = 9-x^2 , y = 0` discover b such the the heat y = b divides the an ar bounded by the graphs the the equations right into two areas of same area.


2 education answers

Math

recent answer post July 13, 2012 at 1:26:05 afternoon


discover the precise area bounded by the curve y=sinx and y=cosx in the domain 0≤x≤2pi


1 educator answer

Math

recent answer post September 16, 2016 in ~ 6:45:38 afternoon


find the centroid that the an ar bounded by the graphs the `y=sqrt(r^2-x^2)` and `y=0`


1 education answer
juniorg8.com will assist you with any kind of book or any kind of question. Our summaries and analyses space written by experts, and your concerns are reply by actual teachers.

join juniorg8.com


apply to be an education

Recommended

More


©2021 juniorg8.com, Inc. All rights Reserved