Evaluate the integral. integral_0^1 (t i + t^2 j + t^3 k) dt.

Question:

Evaluate the integral.

{eq}\displaystyle \int_0^1 (t i + t^2 j + t^3 k)\ dt {/eq}.

Vector Integrals

When we are integrating vector components it is a given rule that they must be integrated separately. reason for this is that all the components are perpendicular to each other and thus will not get in the way of anything.

Answer and Explanation:

Given;

{eq}\displaystyle \int_0^1 (t i + t^2 j + t^3 k)\ dt \\ \displaystyle ( \int_0^1 t dt i + \int_0^1 t^2 dt j + \int_0^1 t^3 dt k ) \ ...

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Using Integration By Parts

from Math 104: Calculus

Chapter 13 / Lesson 7
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