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 $x in [1,2 ]$ ?

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Answer 1 · 2017-12-31T18:31:45

$W= 3+e^2$ Joule

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

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

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