Chapter 8, Integration Video Solutions, Engineering Mathematics Through Applications

Problem 1

Determine the following integrals:
a $\int x \mathrm{~d} x$
$\mathbf{b} \int u^{2} \mathrm{~d} u$
c $\int z^{3} \mathrm{~d} z$
$\mathbf{d} \int t^{1 / 2} \mathrm{~d} t$
e $\int(\omega t) \mathrm{d}(\omega t) \quad \mathbf{f} \int 3 \mathrm{~d} t$
$\mathbf{g} \int t^{-2} \mathrm{~d} t \quad \mathbf{h} \int x^{-1 / 2} \mathrm{~d} x$
For question 2 you may use any appropriate mathametical software.

Morgan Cheatham

Numerade Educator

02:15

Problem 2

Plot the graph of $y=x^{3}$ from $x=0$ to 1 .
i Use the leftbox command to draw four boxes on the graph of $y=x^{3}$. Evaluate the total area of the four boxes by using the leftsum command.
ii Repeat $\mathbf{i}$ for 8 boxes.
iii Repeat $\mathbf{i}$ for 16 boxes.
iv Repeat $\mathbf{i}$ for 32 boxes.
v Repeat $\mathbf{i}$ for 64 boxes.
vi Repeat $\mathbf{i}$ for 128 boxes.
vii By applying the command $\operatorname{evalf}\left(\operatorname{int}\left(x^{\wedge} 3, x=0.1\right)\right)$, evaluate $\int_{0}^{1} x^{3} \mathrm{~d} x .$ What do you notice about your results?

Eric Mockensturm

Numerade Educator

03:12

Problem 3

Determine the shaded areas shown in Fig. 7 below:

Gregory Higby

Numerade Educator