Question
find the total area between the curves ( y= 4-x ^2 ) and the x-axis over the intervals [0,4]
Answers
Reiny
the curve crosses at (2,0), so you have to find the area in 2 parts, from 0 to 2, and then from 2 to 4
area = integral [4-x^2] from 0 to 2 + integral [-4 + x^2] from 2 to 4
= [4x - x^3/3] from 0 to 2 + [-4x + x^3/3] from 2 to 4
= (8-8/3 - 0) + (-16 + 64/3 - (-8 + 8/3))
= 8 - 8/3 - 16 + 64/3 + 8 - 8/3
= 16
check my arithmetic
area = integral [4-x^2] from 0 to 2 + integral [-4 + x^2] from 2 to 4
= [4x - x^3/3] from 0 to 2 + [-4x + x^3/3] from 2 to 4
= (8-8/3 - 0) + (-16 + 64/3 - (-8 + 8/3))
= 8 - 8/3 - 16 + 64/3 + 8 - 8/3
= 16
check my arithmetic