16What is the value of the definite integral(2t/4 + 6) dt? Enter your answer as an exact fraction if necessary.Provide your answer below:

Given, ∫1162t12+6dt We know that, ∫fx±gxdx=∫fxdx±∫gxdx Therefore, ⇒∫1162t12+6dt=∫1162t12dt +∫1166…

Answered: 16 What is the value of the definite…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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16
What is the value of the definite integral
(2t/4 + 6) dt? Enter your answer as an exact fraction if necessary.
Provide your answer below:

Expert Solution

Step 1

Given,

$\int_{1}^{16} (2 t^{\frac{1}{2}} + 6) d t$

We know that,

$\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x$

Therefore,

$\Rightarrow \int_{1}^{16} (2 t^{\frac{1}{2}} + 6) d t = \int_{1}^{16} 2 t^{\frac{1}{2}} d t + \int_{1}^{16} 6 d t \int x^{n} d x = \frac{x^{n + 1}}{n + 1} \int_{1}^{16} 2 t^{\frac{1}{2}} d t = 2 {[\frac{t^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}]}_{1}^{16} = 84 \int_{1}^{16} 6 d t = 6 {[t]}_{1}^{16} = 90$

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