Hi, I need help with this question please, (a) and (b). Please show full work and label every step in your solution that uses FTOC. 5. (a) Show an exemple of a proof or computation that uses the FTOC part 1. Make sure tothe label the step(s) where the theorem is used.(b) Show an exemple of a proof or computation that uses the FTOC part 2. Make sure tothe label the step(s) where the theorem is used.

Answered: 5. (a) Show an exemple of a proof or…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Hi, I need help with this question please, (a) and (b). Please show full work and label every step in your solution that uses FTOC.

5. (a) Show an exemple of a proof or computation that uses the FTOC part 1. Make sure to
the label the step(s) where the theorem is used.
(b) Show an exemple of a proof or computation that uses the FTOC part 2. Make sure to
the label the step(s) where the theorem is used.

Expert Solution

Step 1

Fundamental theorem of calculus part 1:

Let $f (x)$ be a continuous function on an interval $[a, b]$ . The function $F (x)$ is defined as follows,

$F (x) = \int_{a}^{x} f (x) d x$ ,

then $F' (x) = f (x)$ over $[a, b]$ . $F (x)$ is called as anti derivative of $f (x)$ .

Consider the following problem,

Find the function $\frac{d}{d x} \int_{0}^{x} \sin x d x$ .

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5. (a) Show an exemple of a proof or computation that uses the FTOC part 1. Make sure to the label the step(s) where the theorem is used. (b) Show an exemple of a proof or computation that uses the FTOC part 2. Make sure to the label the step(s) where the theorem is used.