# What the area of the figure bounded by the given curve y=(x*(sqrt36-x^2)) (0_< x_< 6)?

##### 1 Answer

May 11, 2018

The area is

#### Explanation:

We have:

#A = int_0^6 xsqrt(36 - x^2)dx#

Now let

#A = int_36^0 xsqrt(u) * (du)/(-2x)#

#A = 1/2int_0^36sqrt(u) du#

#A = 1/2[2/3u^(3/2)]_0^36#

#A = 1/2[2/3(36- x^2)^(3/2)]_0^6#

#A = (1/2)2/3(36 - 0)^(3/2)#

#A = (1/2)144#

#A = 72#

Hopefully this helps!