Question #c6368

1 Answer
Jan 2, 2018

#int_-2^2(1-x^2)dx=-4/3 "units"^2#

Explanation:

Given: #int_-2^2(1-x^2)dx#

Integrate each term separately:

#int# #1dx=1x# OR #x# since #intcdx=cx+"C"#

#int-x^2dx=-x^3/3# since #intx^adx=(x^(a+1))/(a+1)+"C#

Thus we get:

#int_-2^2(1-x^2)dx=[x-x^3/3]_-2^2#

Evaluate the upper/lower limits:

#=[(2)-(2)^3/3]-[(-2)-(-2)^3/3]#

#=[2-8/3]-[-2+8/3]#

#=-4/3 "units"^2#