1. Tardigrade
  2. Question
  3. Mathematics
  4. The area bounded by the curves y=(x+1)2, y=(x+1)2 and y=(1/4) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The area bounded by the curves $y=\left(x+1\right)^{2}$, $y=\left(x+1\right)^{2}$ and $y=\frac{1}{4}$ is

Application of Integrals

Solution:

We have, $y=\left(x + 1 \right)^{2}$ $\, ... \left(i\right)$, parabola with vertex $\left(-1, 0\right)$
and $y = \left(x -1\right)^{2}$ $ \, ... \left(ii\right)$, parabola with vertex $\left(1,0\right)$.
Solving $\left(i\right)$ and $\left(ii\right)$, we get $x = 0$ and $y = 1$
image
Required area $= A =2\int_{\frac{1}{4}}^{1}\left(1-\sqrt{y}\right)dy$
$=2\left[y-\frac{2}{3}y^{3 / 2}\right]_{1/ 4}^{1}$
$=2\left[\frac{3}{4}-\frac{2}{3}\left(1-\frac{1}{8}\right)\right]$
$=\frac{3}{2}-\frac{7}{6}=\frac{1}{3}$ sq. units.