1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ddd [48]
3 years ago
5

Evaluate the integral. (remember to use absolute values where appropriate. Use c for the constant of integration.) 5 cot5(θ) sin

4(θ) dθ
Mathematics
1 answer:
ozzi3 years ago
7 0

I=5\int \frac{cos^{4}\theta }{sin\theta }\times cos\theta d\theta \\\\I=5\int \left ( 1-sin^{2}\theta  \right )^{2}\times \frac{cos\theta }{sin\theta }d\theta \\put\ \sin\theta =t\\\\dt=cos\theta d\theta \\\\I=5\int\frac{t^{4}+1-2t^{2}}{t}dt\ \ \ \ \ \ \ \ \ \ \because (a-b)^2=a^2+b^2-2ab\\\\I=5\left ( \int t^{3}dt + \int \frac{1}{t} -2\int t \right )dt

by using the integration formula

we get,

\\I=5\left ( \frac{t^{4}}{4} +logt -t^{2}\right )\\\\I=\frac{5}{4}t^{4}+5\log t-5t^{2}+c

now put the value of t=\sin\theta in the above equation

we get,

\int 5\cot^5\theta \sin^4\theta d\theta=\frac{5}{4}sin^{4}\theta+5\log \sin\theta - 5sin^{2} \theta+c

hence proved

You might be interested in
What do 89/90 equal but not as a decimal or a percent as a fraction HELP ME
sergeinik [125]

Answer:

it equals 89/90

Step-by-step explanation:

the gcf of 89, 90 is 1, so the fraction can not be simplified. The answer is 89/90.

3 0
3 years ago
What percentage of the area under a normal curve is within 1, 2, and 3 standard deviations of the mean
Lemur [1.5K]

Answer:

You need to have a labotomy sir

Step-by-step explanation:

7 0
2 years ago
What is the value of the expression 10(n-6) when 4=14
Vedmedyk [2.9K]

Answer:

it's going to be 4n so its going to be 4...

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Graph the linear equation using the slope and​ y-intercept.<br> Y=4X+3
JulsSmile [24]

The slope-intercept form: y = mx + b

m - slope

b - y-intercept

We have y = 4x + 3

m = 4 - slope

3 - y-intercept


m=\dfrac{\Delta Y}{\Delta x}\to4=\dfrac{4}{1}

4 units up and 1 unit right

7 0
3 years ago
The slope of the line (2,2) and (6,10) ​
soldi70 [24.7K]

Answer:

2

Step-by-step explanation:

It rose 8 and ran 4 and slope is rise over run.

8/4 = 2

7 0
3 years ago
Other questions:
  • What is the x-value of the solution to this system of equations? x = 2y − 4 7x + 5y = -66
    13·1 answer
  • Alberto conducted an experiment by rolling a fair six-sided number cube 60 times. He rolled a 2 fifteen times. Which statement a
    9·1 answer
  • How do you graph y=3/2x-1
    10·2 answers
  • A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a
    8·2 answers
  • 7 yards = to how many feet
    15·1 answer
  • Clint's salary increased from ​$24000 to $36000 over a​ three-year period.​ Helen's salary increased from ​$29000 to $43, 500 ov
    15·1 answer
  • What is the image point of (-8,7)(−8,7) after a translation right 5 units and up 5 units?
    5·1 answer
  • What is 50 percent times 3 percent plus two plus 7 subtracted by 12?
    6·2 answers
  • That are equal to 4⋅10-3:
    15·1 answer
  • I believe this is 10x but I don’t know
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!