# Indefinite integral of cross product of 2 function

## Homework Statement:

If ##\vec{v} (t)## is a vector function of t, find indefinite integral
$$\int {\left(\vec v \times \frac{d^2 \vec v}{dt^2} dt\right)}$$

## Relevant Equations:

Idk.
I've tried with this work in attachment. i&m not sure of my answer is correct.

#### Attachments

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STEMucator
Homework Helper
The problem statement is not given properly. Can you provide us proper details? If you are computing:

$$\int v \frac{d^2v}{dt^2} dt$$​

You mentioned ##dv = b(t) dt##, and then computed ##v##:

$$v = \frac{dv}{dt}$$​

You know this is inherently not correct, unless the function is specifically ##v(t) = e^t##. Don't forget about generality when writing math proofs, or computing such things.

• Delta2
haruspex
Homework Helper
Gold Member
The problem statement is not given properly. Can you provide us proper details? If you are computing:
$$\int v \frac{d^2v}{dt^2} dt$$​
The thread title says cross product.

Last edited:
haruspex