The force applied against a moving object travelling on a linear path is given by $F (x) = 2 x^{3} + x$ $F(x)= 2x^3+x$ . How much work would it take to move the object over $x \in [2, 4]$ $x in [2, 4]$ ?

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Answer 1 · 2016-08-14T16:25:22

126J

Provided it's a conservative force

$W = \int_{x_{1}}^{x_{2}} F d x$ $W = int_(x_1)^(x_2) Fdx$

$= \int_{2}^{4} (2 x^{3} + x) d x = {[\frac{1}{2} x^{2} (x^{2} + 1)]}_{2}^{2}$ $= int_2^4 (2x^3 + x)dx = [1/2x^2(x^2+ 1)]_2^4$

$= \frac{1}{2} {(4)}^{2} (4^{2} + 1) - \frac{1}{2} {(2)}^{2} (2^{2} + ` 1)$ $=1/2(4)^2(4^2+1) - 1/2(2)^2(2^2+`1)$

$= 8 (17) - 2 (5) = 126$ $=8(17) - 2(5) = 126$

The force applied against a moving object travelling on a linear path is given by F(x)= 2x^3+xF(x)=2x3+xF(x)= 2x^3+x. How much work would it take to move the object over x in [2, 4] x∈[2,4]x in [2, 4] ?