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spin [16.1K]
3 years ago
8

Find the trigonometric integral. (Use C for the constant of integration.)

Mathematics
1 answer:
Olin [163]3 years ago
4 0

Suppose we let u=\sin\theta+\cos\theta, so that \mathrm du=(\cos\theta-\sin\theta)\,\mathrm d\theta.

Also, recall the double angle identity for cosine:

\cos(2\theta)=\cos^2\theta-\sin^2\theta=(\cos\theta-\sin\theta)(\cos\theta+\sin\theta)

So, we can rewrite and compute the integral using the substitution, as

\displaystyle\int\cos(2\theta)(\sin\theta+\cos\theta)^3\,\mathrm d\theta

=\displaystyle\int u\cdot u^3\,\mathrm du

=\displaystyle\int u^4\,\mathrm du

=\dfrac{u^5}5+C

=\boxed{\dfrac{(\cos\theta+\sin\theta)^5}5+C}

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Find the domain and the range of the relation shown in the given graph. Also, determine whether the relation is a function.
Ivahew [28]

Answer:

yes, it is a function

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R: {2, 4}

Step-by-step explanation:

7 0
3 years ago
For a field trip 11 students rode in cars and the rest filled eight buses. Which equation below will help you find how many stud
Helen [10]

Answer:

8x + 11= 315

Step-by-step explanation:

Let x = the number of students in a bus

There are 8 buses

8x is the number of students in buses

There are 11 students in cars

Add this together to get all the students, which is 315

8x + 11= 315

6 0
3 years ago
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three times the lesser of two consecutive even integers is 6 less than six times the greatest number. find the integers.
kakasveta [241]

3x-6=6(x+2)   3x-6=6x+12  3x-6x=6+12   -3x=18  X= 18/-3  X= -6  first number . For second number you substitute x+2. -6+2=-4    

3 0
3 years ago
Solve the following simultaneous equations: 1. a) x-y=-5 and x + y = -1​
Sonbull [250]

Answer:

x = -3, y = 2

Step-by-step explanation:

x - y = -5

x = -5 + y

Let's put this into the other equation

(-5 + y) + y = -1

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2y = 4

y = 2

Now we can solve for x by plugging y into either equation

x + (2) = -1

x = -3

8 0
2 years ago
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Jane has 15 phone cards worth either $20 or $15. How many of each does she have if the phone cards total $245?
mariarad [96]

The correct answer is 12

Hope this helped!

3 0
2 years ago
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