# 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:
STEMucator
Homework Helper

Integrate all the remaining terms, and you get a sum of antiderivatives that subtract from the other terms.

I still dislike how we use X for multiplication, and cross product every time I see it, sorry for the confusion.

haruspex