When a particle is located at a distance x feet from the origin, a force of x +2x pounds acts on it. How much work is done in moving it from x= 1 to x= 2?
Optimization
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Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
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Volume
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We have the given Force function F(x) =
where x is the distance in feet from the origin.
Work done (dW) in displacement of a particle by dx (i.e from x to x+dx) units is given by-
Work = Force × Displacement
dW = F(x) dx
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