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F(2) = | (t + 2) dt. %3D

F(2) = | (t + 2) dt. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Define F(x) = 3. (t +2) dt. Draw a graph that shows the area represented by the definite integral +2) dt. EXPLAIN how to use geometry to find a formula for the EXACT value of (b) this area. That is, find a formula for F(x) and show all steps. (c) Now find F'(x). Is the answer what you expected? Explain.
Transcribed Image Text:Define F(x) = 3. (t +2) dt. Draw a graph that shows the area represented by the definite integral +2) dt. EXPLAIN how to use geometry to find a formula for the EXACT value of (b) this area. That is, find a formula for F(x) and show all steps. (c) Now find F'(x). Is the answer what you expected? Explain.
Expert Solution
Step 1

Given

F(x)=∫0x(t+2)dt

Step 2

(a)

The function to be integrated is y = x+2 and limits of integration can be expressed by the interval [0,x] that is x≥0

This area bounded by the integral  F(x)=∫0x(t+2)dt is graphically expressed as 

Advanced Math homework question answer, step 2, image 1

The area represented by the given integral is the area of the shaded region.

steps

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