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

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

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Answer 1 · 2016-02-13T14:40:16

$W = 6 e^{7} - 2 e^{3}$ $W=6e^7-2e^3$

Explanation:

$W = \int_{3}^{7} (1 + x e^{x}) d x$ $W=int _3^7 (1+x e^x )d x$
$W = {[e^{x} (x - 1)]}_{3}^{x}$ $W=[e^x(x-1)]_3^7$
$W = [e^{7} (7 - 1)] - [e^{3} (3 - 1)]$ $W=[e^7(7-1)]-[e^3(3-1)]$
$W = 6 e^{7} - 2 e^{3}$ $W=6e^7-2e^3$

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

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

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Explanation:

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