Class 12

Math

Calculus

Application of Integrals

Sketch the region lying in the first quadrant and bounded by $y=9x_{2}$, $x=0$, $y=1$ and $y=4$. Find the area of the region, using integration.

Similarly $x_{2}=9y $ has even power of $y$ and is symmetrical about $y−axis$

So the required area is written as

Required area $=∫_{1}xdy$

$=∫_{1}3y dy$

$=31 [3/2y_{3/2} ]_{1}$

$=92 [4_{3/2}−1_{3/2}]$

$=92 (8−1)$

$=914 $ sq. units.