x/2 1. Let F(x) = | f(t) dt and G(x) = | g(t) dt, where the graphs of f(x) and g(x) on [0, 6] are below. 4 3.5 3 y = f(x) y = g(x) 1 0.5 1 2 3 6. (i) Evaluate 9(f(t) + 1)f'(t) dt. L In(2) . I (Im(z)) dr. g' (In(x)) dæ. (ii) Evaluate c12 (iii) Evaluate F(G(z))g () da.

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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px/2
1. Let F(x) = | f(t) dt and G(æ) = | g(t) dt, where the graphs of f(x) and g(x) on [0, 6] are below.
4
3.5
3
y = f(x)
2
y = g(x)
1
0.5
1
3
4
(i) Evaluate
| 9(f(t) + 1)f'(t) dt.
In(x) ·
9ʻ(In(x)).
(ii) Evaluate
dxr.
e3
c12
(iii) Evaluate
| F(G(x))g(5)
dx.
Transcribed Image Text:px/2 1. Let F(x) = | f(t) dt and G(æ) = | g(t) dt, where the graphs of f(x) and g(x) on [0, 6] are below. 4 3.5 3 y = f(x) 2 y = g(x) 1 0.5 1 3 4 (i) Evaluate | 9(f(t) + 1)f'(t) dt. In(x) · 9ʻ(In(x)). (ii) Evaluate dxr. e3 c12 (iii) Evaluate | F(G(x))g(5) dx.
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