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Attached below is a pdf of the questions I need answered. Please show the work. Thanks in advance.
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Class Work 14.1
MAT 210
Name__________________________
Integration by Parts
∫ u dv = uv − ∫ v du
∫ xe
dx
let u = x
dv = e x dx
= xe x − ∫ e x dx
du = dx
v = ex
x
= xe x − e x + C
Evaluate the following integrals
1.
∫ xe
3.
∫ x ln x dx
5.
∫x
−x
2
dx
e − x dx
2.
∫ x(x + 1) dx
4.
∫ (x + 1)e
8
2x
dx
MAT 210
Class Work 14.2
Name__________________________
Area Between Two Curves
If f ( x ) ≥ g ( x ) for all x in [a , b] , then the area of the region between
the graphs of f and g between x = a and x = b is given by
b
∫ [ f (x ) − g (x )]dx
a
1. Find the area of the region bounded by the curves f ( x ) = x 2 − 2 x and f ( x ) = − x 2 + 4
2. Find the total area between the curves y = x 3 and y = 4 x .
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