area between curves

**gracey** · March 9th 2008, 08:35 AM

find the area enclosed by the curves y= x^2 + 7 and y= 2x^2 +3

thanks

**galactus** · March 9th 2008, 09:35 AM

Equate the functionsto find the limits of integration.

Then we get:

$\int_{-2}^{2}\left[(x^{2}+7)-(2x^{2}+3)\right]dx$

**Krizalid** · March 9th 2008, 10:51 AM

Let $f(x)=x^2+7$ & $h(x)=2x^2+3.$

These curves intersect at $f(x)=h(x),$ this yields $[-2,2].$ We need to integrate a certain function in such interval. We have $f(x)\ge h(x),$ and so our integral is

$\int_{ - 2}^2 {\left\{ {\left( {x^2 + 7} \right) - \left( {2x^2 + 3} \right)} \right\}\,dx} ,$ which confirms galactus' result.

(Exploiting the symmetry saves time on calculations.)

Thread: area between curves

LinkBack

Thread Tools

Display

area between curves

Similar Math Help Forum Discussions

Area between Curves

Area between two curves

area between curves.

Area Between Two Curves

Area between two curves

Search Tags