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The force applied against a moving object travelling on a linear path is given by #F(x)=3xe^x #. How much work would it take to move the object over #x in [2, 7] #?

The force applied against a moving object travelling on a linear path is given by #F(x)=3xe^x #. How much work would it take to move the object over #x in [2, 7] #?
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ReportAnswer #1

I got: #W=19,717J#

Explanation:

Here you have a variable force (changes with distance #x#) so to evaluate the Work we need to use the integral version as:

#W=int_(x_1)^(x_2)F(x)dx#

or, in your case:

#W=int_2^7(3xe^x)dx=# by parts:

#=3[xe^x-e^x]# between #x=2# and #x=7# gives you:

#W=19,717J#

answered by: GiĆ³
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The force applied against a moving object travelling on a linear path is given by #F(x)=3xe^x #. How much work would it take to move the object over #x in [2, 7] #?
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