The factor I desire to carry out this is to calculation the area between this curve, the y-axis, y=5 and y=1.

You are watching: X in terms of y

I found the answer to it is in 5 making use of a roundabout method.

But my very first attempt to be to shot and express x in terms of y.

Basic algebra provided me one expression v an $x^3$.


I think that this will get really confusing if you incorporate with respect come y.

Here is what I suggest you do.

$y = 2x + \frac 8x^2 -5$

Evaluated in ~ $y = 1$ and also $y = 5$

$1 = 2x + \frac 8x^2 -5\\x = 2$

$5 = 2x + \frac 8x^2 -5\\x = 1$

$\int_0^1 (5-1) \;dx + \int_1^2 2x + \frac 8x^2 -5 - 1\;dx$


Basic algebra is correct.

From$y=2x+\frac8x^2-5$,multiplying by $x^2$we get$yx^2=2x^3+8-5x^2$,or$2x^3-(5-y)x^2+8= 0$.

This is,unfortunately,a cubicwhich can be resolved by thetraditionally confusing formula.

Its derivative is$6x^2-2(5-y)x= 0$which has roots$x=0$and$x=\dfrac5-y3$.

Note thatat $x=0$the duty is $8$and at$\dfrac5-y3$the value is$2(\frac5-y3)^3-(5-y)(\frac5-y3)^2+8=(\frac5-y3)^3(2-3)+8=-(\frac5-y3)^3+8=(\fracy-53)^3+8$.From this,we can determine whichvalues of $y$give one equation with$1$ or $3$ genuine roots.

point out
reply Dec 13 "16 at 20:56

marty cohenmarty cohen
98.2k88 yellow badges6464 silver badges156156 bronze title
add a comment |
To find the area, there isn"t a certain reason to uncover $x$ in regards to $y$. A graph of the role shows that the area is relatively simple to find.


You just have actually to discover the area under your duty from $1$ come $2$ (you can use the basic Theorem of Calculus here), and also manipulate it to gain your desired area.

answered Dec 13 "16 at 20:58

34411 silver badge99 bronze title
add a comment |

your Answer

Thanks because that contributing solution to rwandachamber.orgematics stack Exchange!

Please be sure to answer the question. Carry out details and share your research!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based upon opinion; back them increase with references or an individual experience.

Use rwandachamber.orgJax to format equations. Rwandachamber.orgJax reference.

To find out more, see our tips on writing an excellent answers.

See more: Axis And Allies Ww1 - Axis And Allies 1914 World War I Board Game

Draft saved
Draft discarded

Sign increase or log in in

sign up utilizing Google
sign up making use of Facebook
authorize up making use of Email and also Password

Post together a guest

email Required, yet never shown

Post as a guest


Required, yet never shown

short article Your price Discard

By click “Post your Answer”, girlfriend agree to our regards to service, privacy policy and cookie plan

Not the answer you're spring for? Browse other questions tagged integration algebra-precalculus or ask your own question.

Featured on Meta
Visit conversation
What am i misunderstanding around this straightforward integral question? (Area under a curve)
find the area fastened by the complying with curve.
Area between a curve, x axis and a heat
exercise in algebra - Express various terms
very first order differential equation - area.
Area between two curves. Separation so that it is equal.
identify integration borders for the complying with region.
utilizing Newton-Raphson method, discover the solution for $e^\fracx^24vt = 1+\fracx^22vt$
hot Network inquiries an ext hot concerns

concern feed
i ordered it to RSS
inquiry feed To subscribe to this RSS feed, copy and also paste this URL into your RSS reader.


ridge Exchange Network
site style / logo design © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.9.17.40233

rwandachamber.orgematics stack Exchange works finest with JavaScript allowed

her privacy

By clicking “Accept all cookies”, girlfriend agree stack Exchange can store cookie on your machine and disclose details in accordance through our Cookie Policy.