Purchase Solution

Calculus Review on Integrals

Not what you're looking for?

Ask Custom Question

1. Evaluate the following indefinite integrals:

See attached

2. On a dark night in 1915, a German zeppelin bomber drifts menacingly over London. The men on the ground train a spotlight on the airship, which is traveling at 90 km/hour, and at a constant altitude of 1 km. The beam of the spotlight makes an angle θ with the ground.

1. Draw a diagram of the situation.
2. When the airship is 3 kilometers from the spotlight, how fast is θ changing?
3. An electrical circuit consists of two parallel resistors, with resistances R1 and R2 respectively. The total resistance R of the circuit (measured in Ohms Ω) is specified by

See attached

Attachments
Purchase this Solution

Solution Summary

The expert evaluates indefinite integrals in calculus. A diagram is drawn for a situation.

Solution Preview

Please see attachments

In these questions, we use the following formula:
∫▒〖x^n dx=x^(n+1)/(n+1)+c〗
(1)∫▒〖1/x^2 dx=-1/x+c〗
(2)∫▒〖e^(-x) dx=-e^(-x)+c〗
(3)∫▒〖sin⁡(t) cos⁡(t)dt=∫▒〖sin⁡(2t)/2 dt=sin⁡(2t)/4+c〗〗
Assume x=cos(t), dx=-sintdt,
Therefore, ∫▒〖sin⁡(t) cos⁡(t)dt=∫▒〖-xdx=-x^2/2+c〗〗=-(cost)^2/2+c
(4)∫▒〖s^(1/2) ds=s^(1/2+1)/(1/2+1)+c=2/3 s^(3/2)+c〗

2.)

First, we find out the relationship between x and θ,
Then we consider x and θ are functions of t,
After this assumption, we could do derivative on both sides for equation: tan(θ)=1/x
Tan(θ)=1/x,sec^2⁡〖θ*dθ/dt=-(1/x^2 dx)/dt〗
X=sqrt(3^2-1^2)=sqrt(8), dx/dt=90
Sec^2(θ)=1/(sqrt(8)/9)^2 =81/8
dθ/dt=-1/8*(81/8)*90=-113.91

1/R=1/R1+1/R2, when R1=80, R2=100, R=44.444
to find out the change rate for R,we consider ...

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.