Question 13.8: Find the area under z(t ) = e^2t from t = 1 to t = 3....
Find the area under z(t ) = e^{2t} from t = 1 to t = 3.
Step-by-Step
\begin{aligned}\text { Area } & =\int_1^3 z \mathrm{~d} t=\int_1^3 \mathrm{e}^{2 t} \mathrm{~d} t=\left[\frac{\mathrm{e}^{2 t}}{2}\right]_1^3 \\& =\left[\frac{\mathrm{e}^6}{2}\right]-\left[\frac{\mathrm{e}^2}{2}\right]=198\end{aligned}
Related Answered Questions
Question: 13.11
Verified Answer:
Figure 13.13 illustrates the required area. From t...
Question: 13.10
Verified Answer:
(a) A graph of y = sin x between x = −π and x = π ...
Question: 13.9
Verified Answer:
Figure 13.11 illustrates the required area.
[latex...
Question: 13.7
Verified Answer:
(a) Let I stand for \int_1^2 x^2+1 d x[/la...
Question: 13.6
Verified Answer:
(a) Using the identities in Table 3.1 we find
[lat...
Question: 13.5
Verified Answer:
Powers of trigonometric functions, for example [l...
Question: 13.4
Verified Answer:
(a) \int x^2+9 \mathrm{~d} x=\int x^2 \math...
Question: 13.3
Verified Answer:
(a) From Table 13.1, we find \int x^n \mat...
Question: 13.2
Verified Answer:
From Table 10.1 we find
\frac{\mathrm{d}}{\...
Question: 13.1
Verified Answer:
We need to find a function which, when differentia...