Area between parabola and a line that don't intersect? 0 or infinity

Mathematics Asked on January 5, 2022

Came across a problem on social media,

Find the area of the region bounded by a parabola, $y = x^2 + 6$ and
line a line $y = 2x + 1$.

I tried to draw it on paper and they didn’t seem to intersect. So I drew them online (attached screenshot). My answer was 0, but someone said that we assume they meet at infinity and answer would be infinity. Parallel lines don’t diverge like these do, so I think we can assume that they would never interest at infinity.

enter image description here

One Answer

$$x^2 + 6 = 2x + 1$$ $$x^2 - 2x + 5$$ $$frac{2 pm sqrt{4 - 4(5)}}{2}$$

As you can see by analyzing the discriminant, this quadratic has no real roots, so there are no points at which the two curves intersect. You could say that the area between the curves tends to infinity. As was stated in the comments, whoever posted this most likely intended to include more information/restrictions.

Also, these two curves will not "meet at infinity." Both diverge as $x$ gets arbitrarily large

Answered by N. Bar on January 5, 2022

Add your own answers!

Related Questions

Vector field divergence equivalent definition

0  Asked on August 13, 2020 by user_hello1


Proof of The Third Isomorphism Theorem

1  Asked on August 12, 2020 by abhijeet-vats


Show estimator is consistent

1  Asked on August 8, 2020 by m1996rg


mean distance between three point

0  Asked on August 6, 2020 by yaniv765


Evaluate $int frac{2-x^3}{(1+x^3)^{3/2}} dx$

4  Asked on August 5, 2020 by dharmendra-singh


Nimber multiplication

2  Asked on July 30, 2020 by yberman


Ask a Question

Get help from others!

© 2023 All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP