3. (a) Use the Fundamental Theorem of Calculus to determine a continuous function f: 2. x) -R that satisfies tf(t) dt = 3.r² –. sin? r - 12 + sin? 2 for all r> 2. Verify that your answer is correct by computing the integral tf(t) dt once you have deter- mined the function f. (b) Let 0< c
3. (a) Use the Fundamental Theorem of Calculus to determine a continuous function f: 2. x) -R that satisfies tf(t) dt = 3.r² –. sin? r - 12 + sin? 2 for all r> 2. Verify that your answer is correct by computing the integral tf(t) dt once you have deter- mined the function f. (b) Let 0< c
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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Question
![3. (a) Use the Fundamental Theorem of Calculus to determine a continuous function f : 2,0) → R
that satisfies
| tf(t) dt = 3 - sin?r – 12 + sin 2
- 12 + sin² 2
3r2
for all x 2.
Verify that your answer is correct by computing the integral
tf(t) dt once you have deter-
mined the function f.
(b) Let 0 <c<d and let G: c. d H R be defined as
G(r):=
dt (r E (c, d]).
1 + 1
Justifying all steps, use the Fundamental Theorem of Calculus to express G'(r) in terms of G(r)
and expressions involving r.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23c82962-fdd3-4aae-a199-ce5241f64aad%2Fd899424c-b401-4794-a56d-a1eff321fa76%2Fmr8xg1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. (a) Use the Fundamental Theorem of Calculus to determine a continuous function f : 2,0) → R
that satisfies
| tf(t) dt = 3 - sin?r – 12 + sin 2
- 12 + sin² 2
3r2
for all x 2.
Verify that your answer is correct by computing the integral
tf(t) dt once you have deter-
mined the function f.
(b) Let 0 <c<d and let G: c. d H R be defined as
G(r):=
dt (r E (c, d]).
1 + 1
Justifying all steps, use the Fundamental Theorem of Calculus to express G'(r) in terms of G(r)
and expressions involving r.
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