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b. Find the area of the region bounded by Y = xeax and the x-axis on the interval 0,41, where a> 0.The area is(Type an exact answer.)

Question
b. Find the area of the region bounded by Y = xe
ax and the x-axis on the interval 0,41, where a> 0.
The area is
(Type an exact answer.)
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b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0. The area is (Type an exact answer.)

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Step 1

Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.

Here.fis continuous on [a,b] and f(x)20 on [a,b]
the area of the region bounded
by graph of fand horizontal line on [a,b] is A = [ /(x)dx
A -xe
xedr
u=x
du dx
dv= fedx
1 =
-a
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Here.fis continuous on [a,b] and f(x)20 on [a,b] the area of the region bounded by graph of fand horizontal line on [a,b] is A = [ /(x)dx A -xe xedr u=x du dx dv= fedx 1 = -a

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Step 2

Using integral by parts to s...

A-ve
w-/vdu
-COx
xedx
=uv
-dx
0a
-a
4
-ax
1
хе
-a
-a
-ax
-ax
хе
2.
a
-a
0
-4a
0
4ea
e
a2
-a
-a
-4a
e
-4ae
a2
-4a
+
a2
a2
+1]
e
-4 a
-4ae
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A-ve w-/vdu -COx xedx =uv -dx 0a -a 4 -ax 1 хе -a -a -ax -ax хе 2. a -a 0 -4a 0 4ea e a2 -a -a -4a e -4ae a2 -4a + a2 a2 +1] e -4 a -4ae

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Tagged in

Math

Calculus

Integration

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