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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Finding an Antiderivative In Exercises 53-58, find r( t) that satisfies the initial condition(s).

r ' ( t ) = 4 e 2 t i + 3 e t j , r ( 0 ) = 2 i

To determine

To calculate: The function r(t), where r(t)=4e2ti+3etj satisfying the initial condition r(0)=2i.

Explanation

Given:

The derivative of vector valued function is r(t)=4e2ti+3etj.

And the initial condition is r(0)=2i.

Formula used:

If r(t)=f(t)i+g(t)j+h(t)k, where f, g, and h are continuous function on [a,b], then the definite integral of r is:

abr(t)dt=[abf(t)dt]i+[abg(t)dt]j+[abh(t)dt]k

Calculation:

Consider the following derivative:

r(t)=4e2ti+3etj

Evaluate the integration of the function as follows:

r(t)=r(t)dt=(4e2tdt)i+(3et<

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Chapter 12 Solutions

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