I have a homework problem that deals with solving the integral of a given vector. It sets the vector equal to an equation and then puts it inside of a definite integral and calls this a new vector $\vec{r}$, representing the displacement. I know that I should solve for the integral, but when I did, the answer was incorrect. Is there something that I am missing?

Here is the problem:

After a ball rolls off the edge of a horizontal table at time $t = 0$, its velocity as a function of time is given by: $$\vec{v} = 1.0 \hat{i} − 9.8t \hat{j}$$ where $v$ is in meters per second and $t$ is in seconds. The ball's displacement away from the edge of the table, during the time interval of $0.320\mathrm{s}$ for which the ball is in flight, is given by: $\vec{Δr}$ = the integral from $0.320$ to $0$ of $v dt$.

To perform the integral, you can use the calculus theorem The integral of $[A + B f(x)] dx$ = the integral of $A dx + B$ times the integral $f(x) dx$.

You can think of the units and unit vectors as constants, represented by $A$ and $B$. Perform the integration to calculate the displacement of the ball from the edge of the table at $0.320\mathrm{s}$.


closed as off-topic by user108787, ACuriousMind, Gert, John Rennie, Qmechanic Sep 3 '16 at 14:26

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You may proceed to calculate $\Delta \vec r(t) = \int_{0}^t dt'\,\vec v(t)$ via standard integration. Note that the integral is applied to each component of the velocity vector: $\int dt\,\vec v(t) = (\int dt\,v_x(t),\int dt\, v_y(t))$.


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