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Yuliya22 [10]
3 years ago
12

Find the area between y=(x-2)ex and the x-axis from x=2 to x=4.

Mathematics
1 answer:
mojhsa [17]3 years ago
3 0

Answer:

e^4+e^2

Step-by-step explanation:

It can be found by integral.

First let's find the intersection points.

(x-2)e^x = 0

Only intersection point is x = 2.

And it is asked to find the area in the interval (2, 4).

\int\limits^4_2 (x-2)e^x \,dx=?

We will use integration by parts.

x-2=u\\dx=du\\e^xdx=dv\\e^x=v

\int\limits^4_2 (x-2)e^x \,dx=uv-\int vdu=(x-2)e^x-\int e^xdx=(x-2)e^x-e^x=\\\\=(x-3)e^x|^4_2=(4-3)e^4-(2-3)e^2=e^4+e^2

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