Solve my College problem. Here is a photo.

College

Answered question

2022-05-12

Answer & Explanation

Nick Camelot

Skilled2023-05-07Added 164 answers

To solve

\int \sec u d u

, we use the substitution

v = \tan u + \sec u

. Then,

d v / d x = \sec^{2} u + \tan u \sec u = \sec u (\tan u + \sec u) = \sec u (v)

. Thus,

d u = d v / \sec u (v)

, and

\int \sec u d u = \int \frac{\sec u}{\sec u (\tan u + \sec u)} d v

= \int \frac{1}{v} d v

= \ln | v | + c

= \ln | \tan u + \sec u | + c .

Therefore,

\int \sec u d u = \ln | \tan u + \sec u | + c .

We can check this result by differentiating both sides with respect to

u

and using the identity

\frac{d}{d x} \ln | x | = \frac{1}{x}

\frac{d}{d u} (\ln | \tan u + \sec u | + c) & = \frac{1}{\tan u + \sec u} \cdot (\sec u \tan u + \sec^{2} u)

= \frac{1}{\tan u + \sec u} \cdot \sec u (\tan u + \sec u)

= \sec u,

which is the integrand we started with. Thus, our result is correct.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College

Question 71
a simple binary communication channel carries messages by using only two signals; say 0 and 1. We assume that; for a given binary channel, 40% of the time a 1 is transmitted; the probability that a transmitted 0 is correctly received is 0.90,and the probability that a transmitted 1 is correctly received is 0.95. given 1 is received, probability that 1 was transmitted
The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).
My newspaper is delivered late 60 percent of the time. Suppose deliveries can be described as a Bernoulli process and define a random variable X to be the number of late deliveries per year (365 days). Find the mean and standard deviation of X
My newspaper is delivered late 60 percent of the time. Suppose deliveries can be described as a Bernoulli process and define a random variable X to be the number of late deliveries per year (365 days).
i) Find the mean of X and the standard deviation of X
Jordan Decomposition:
Use the method of substitution to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction for
${\begin{array}{r} y = - 10 \\ 7 x + 3 y = - 23 \end{array}$
SHOW ALL WORK. FOLLOW INSTRUCTIONS CAREFULLY PLEASE
Determine whether the series converges or diverges...
The line through the point $(1,0,6)$ (1,0,6) and perpendicular to the plane $x+3y+z=5$ x+3y+z=5 has vector equation $\underline{r}=\langle u,v,w \rangle =\langle a,b,c \rangle + t \langle d,e,f \rangle$ r=⟨u,v,w⟩=⟨a,b,c⟩+t⟨d,e,f⟩, with $t \in \mathbb{R}$ t∈R.
Two minor league baseball players got a total of 368 hits. Washington had 4
more hits than Sanchez. Find the number of hits for each player.
Two minor league baseball players got a total of 368 hits. Washington had 4 more hits than Sanchez. Find the number of hits for each player.
Show that union of two at most countable sets is atmost countable

Didn't find what you were looking for?