(1) Integrate the following functions: (a) I = [ (4x³ − 6x² + 2x²³¹′)dx (²-3)dx 2 (b) I = .3 (c) I = [ (10 cos(5x) - 2 sin(4x)) da √ (4e²z (d) I = = (4e²x + 6e-2x) dx (2) Find the original function f(x) given f'(x) = 2 - and f(−1) = 7. x (3) Find the original function f(x) given f'(x) = 10 cos(5x)-2 sin(4x) and f(T) = 1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(1) Integrate the following functions:
(a) I = [ (4x³ − 6x² + 2x²³¹′)dx
(²-3)dx
2
(b) I =
.3
(c) I = [ (10 cos(5x) - 2 sin(4x)) da
√ (4e²z
(d) I = =
(4e²x + 6e-2x) dx
(2) Find the original function f(x) given f'(x) = 2 - and f(−1) = 7.
x
(3) Find the original function f(x) given f'(x) = 10 cos(5x)-2 sin(4x) and f(T) = 1.
Transcribed Image Text:(1) Integrate the following functions: (a) I = [ (4x³ − 6x² + 2x²³¹′)dx (²-3)dx 2 (b) I = .3 (c) I = [ (10 cos(5x) - 2 sin(4x)) da √ (4e²z (d) I = = (4e²x + 6e-2x) dx (2) Find the original function f(x) given f'(x) = 2 - and f(−1) = 7. x (3) Find the original function f(x) given f'(x) = 10 cos(5x)-2 sin(4x) and f(T) = 1.
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