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

1 Answer
Dec 31, 2017

Answer:

#W= 3+e^2# Joule

Explanation:

#F(x) = 2x+xe^x#

As we know,

#dW= vec F * vec(dx)#

Integrating both sides

#W= int_1^2(2x+xe^x)dx#

#W= [x^2]_1^2+int_1^2xe^xdx#

Applying by-parts by ILATE rule,

#W= [x^2]_1^2+[xe^x]_1^2-int_1^2e^xdx#

#W= [x^2]_1^2+[xe^x]_1^2-[e^x]_1^2#

#W= 4-1+2e^2-e-e^2+e# Joule

#W= 3+e^2# Joule