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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Evaluate the integral, if it exists.

0 1 sin ( 3 π t ) d t

To determine

The value of the integral function.

Explanation

Given information:

The integral function is 01sin(3πt)dt

The region lies between x=0 and x=1.

Calculation:

Consider (3πt) as u.

u=3πt (1)

Differentiate both sides of the Equation.

du=3πdt (2)

Rearrange equation (2) to find the value of dt as shown below:

dt=13πdu (3)

Calculate the lower limit value of u using Equation (1).

Substitute 0 for t in Equation (1).

u=3π×0=0

Calculate the upper limit value of u using Equation (1).

Substitute 1 for t in Equation (1).

u=3π×1=3π

Substitute u for (3πt) and 13πdu for dt in the given integral function as shown below:

01sin(3πt)dt=03πsinu(13π<

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