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## Main Question or Discussion Point

I’m having trouble understanding the relationship between how work is both a dot product and integral. I know that work equals F • D and also the integral of F(x): the area under the curve of F and D.

However, let’s say that I have a force vector <3,4> and a displacement vector of <3,0>. The dot product yields 9J.

However, if I took the area under the curve by treating the vector <3,4> as a line segment which has a magnitude of 5 and the displacement vector also as a line segment with magnitude 3, then the area under the curve of this triangle with side lengths 3, 4, and 5 give me an area of 6J.

Does anyone know what I’m doing wrong?

However, let’s say that I have a force vector <3,4> and a displacement vector of <3,0>. The dot product yields 9J.

However, if I took the area under the curve by treating the vector <3,4> as a line segment which has a magnitude of 5 and the displacement vector also as a line segment with magnitude 3, then the area under the curve of this triangle with side lengths 3, 4, and 5 give me an area of 6J.

Does anyone know what I’m doing wrong?