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
uranmaximum [27]
3 years ago
9

Evaluate the following integrals: 1. Z x 4 ln x dx 2. Z arcsin y dy 3. Z e −θ cos(3θ) dθ 4. Z 1 0 x 3 √ 4 + x 2 dx 5. Z π/8 0 co

s4 (2x) dx 6. Z sin3 x dx 7. Z sec4 x tan3 x dx 8. Z tan5 x sec x dx
Mathematics
1 answer:
Zigmanuir [339]3 years ago
6 0

Answer:

The integrals was calculated.

Step-by-step explanation:

We calculate integrals, and we get:

1) ∫ x^4 ln(x) dx=\frac{x^5 · ln(x)}{5} - \frac{x^5}{25}

2) ∫ arcsin(y) dy= y arcsin(y)+\sqrt{1-y²}

3) ∫ e^{-θ} cos(3θ) dθ = \frac{e^{-θ} ( 3sin(3θ)-cos(3θ) )}{10}

4) \int\limits^1_0 {x^3 · \sqrt{4+x^2} } \, dx = \frac{x²(x²+4)^{3/2}}{5} - \frac{8(x²+4)^{3/2}}{15} = \frac{64}{15} - \frac{5^{3/2}}{3}

5)  \int\limits^{π/8}_0 {cos^4 (2x) } \, dx =\frac{sin(8x} + 8sin(4x)+24x}{6}=

=\frac{3π+8}{64}

6)  ∫ sin^3 (x) dx = \frac{cos^3 (x)}{3} - cos x

7) ∫ sec^4 (x) tan^3 (x) dx = \frac{tan^6(x)}{6} + \frac{tan^4(x)}{4}

8)  ∫ tan^5 (x) sec(x)  dx = \frac{sec^5 (x)}{5} -\frac{2sec^3 (x)}{3}+ sec x

You might be interested in
If it takes 6 hours for a plane to travel 720km with a tail wind and 8 hours to make the return trip with a head wind. Find the
denis-greek [22]

The speed of wind and plane are 105 kmph and 15 kmph respectively.

<u>Solution:</u>

Given, it takes 6 hours for a plane to travel 720 km with a tail wind and 8 hours to make the return trip with a head wind.  

We have to find the air speed of the plane and speed of the wind.

Now, let the speed wind be "a" and speed of aeroplane be "b"

And, we know that, distance = speed x time.

\text { Now, at tail wind } \rightarrow 720=(a+b) \times 6 \rightarrow a+b=\frac{720}{6} \rightarrow a+b=120 \rightarrow(1)

Now at head wind → 720=(a-b) \times 8 \rightarrow a-b=\frac{720}{8} \rightarrow a-b=90 \rightarrow(2)

So, solve (1) and (2) by addition

2a = 210

a = 105

substitute a value in (1) ⇒ 105 + b = 120

⇒ b = 120 – 105 ⇒ b = 15.

Here, relative speed of plane during tail wind is 120 kmph and during head wind is 90 kmph.

Hence, speed of wind and plane are 105 kmph and 15 kmph respectively.

6 0
3 years ago
Find a function for the graph below
Zinaida [17]

Answer:

d

Step-by-step explanation:

gfstikuhbbcwdjonngbb1519360

6 0
3 years ago
Read 2 more answers
Please answer as soon as possible
OlgaM077 [116]

Answer:

  • 30 cubic units³

Step-by-step explanation:

<u>Given equation:</u>

  • 3 * 2 * 5

<u>Solve for cubic units³</u>

  • 3 * 2 * 5
  • = 6 * 5
  • = 30

There are 30 cubic inches³.

<u>Word form:</u>

  • Three times Two Times Five
  • equals Six times Five
  • equals Thirty.

There are Thirty cubic inches³.

7 0
1 year ago
Read 2 more answers
camryn mason obtained a $1,200 loan for her scuba diving lessons. She borrowed the money for six months at 7% interest. Her mont
SVEN [57.7K]

Answer:

3.4296913278%

Step-by-step explanation:

1200-204.10 =996.9

7

204.1

x 100% = 3.4296913278% Theres probably another way to do this and im pretty sure this is correct

8 0
2 years ago
X2 - 10x - 56 = 0 quadratics
slava [35]

Answer:

Step-by-step explanation:

casbheq3

6 0
2 years ago
Other questions:
  • Can someone please help?​
    14·1 answer
  • If the ratio of areas of two similar polygons is 25:49, what is the ratio of the corresponding side lengths
    9·1 answer
  • The graph shows the distance Julian drives on a trip. What is Julian’s speed
    10·2 answers
  • A right triangle. A side is StartRoot 34 EndRoot meters and the hypotenuse is 9 meters.
    12·1 answer
  • to the nearest thousandth what is the cosine of the angle formed by the line whose equation is y=2x and the positive x axis
    14·1 answer
  • What does "E" mean in math when you answer a queastion?
    10·2 answers
  • 7.8y + 2 = 165.8 show work
    9·2 answers
  • Use the x-intercept method to find all real solutions of the equation x^3-10x^2+17x+28=0
    15·2 answers
  • Please help me simplify the expression where possible. (r-3s2t)4
    6·1 answer
  • Is 9, 16, 23, 30, an arthmetic sequence
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!