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aivan3 [116]
3 years ago
15

Integration of ∫(cos3x+3sinx)dx ​

Mathematics
1 answer:
Murljashka [212]3 years ago
6 0

Answer:

\boxed{\pink{\tt I =  \dfrac{1}{3}sin(3x)  - 3cos(x) + C}}

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\  dx

  • Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .
  • Now , Rewrite using du and u .

\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I =  \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I =  \dfrac{1}{3}sin(3x)  - 3cos(x) + C }}}}}

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Solve for the values of x and y in each item to make the given quadrillater a parallelogram​
maria [59]

Answer:

For given parallelogram, the value of x = 114° and y = 66°

Step-by-step explanation:

(Refer figure)

Given quadrilateral ABCD is a parallelogram.

m∠A = 66°

m∠B = x°

m∠C = y°

m∠D = 114°

Since by properties of parallelogram, the both pairs of opposite sides of a parallelogram are parallel.

Opposite angles of a parallelogram are congruent ...........................(1)

Consecutive angles of a parallelogram are supplementary ................(2)

Using (1) for given parallelogram ABCD; we get,

m∠B = m∠D

m∠A = m∠C

Therefore x = 114° and y = 66°.

Using (2) to check whether the two consecutive angles are supplementary.

( m∠A + m∠D ) =  ( m∠B + m∠C ) = ( m∠C + m∠D ) = 66° + 114° = 180°

Hope it helps!!

3 0
3 years ago
Find the area of rectangular ground of length the25√3m and breath 20√6m<br>​
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Answer: 500√18

Step-by-step explanation:

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Length = 25√3m

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Therefore 500√18m is the are of the ground.

Answer From GauthMath if you like it please Heart and comment thanks.

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3 years ago
Someone please help me
MariettaO [177]

Hey there! I'm happy to help!

Let's think of this as the equation y=mx+b, where m represents the slope and b equals the y-intercept.

The y-intercept is where the line hits the y-axis. As we can see, it hits it at the y-value of zero. Therefore, our equation is just left as y=mx now because b is 0.

We want to find the slope now. This is known as the rise/run, or the y/x. This is basically saying how far up it goes for every one step to the right. If we go to the x-value of one, we see that the y-value is at a little bit less than one. We want to keep on moving to the right until the y-value is at a nice integer value (number without fractions).

If we keep on moving to the right, we see that at the x-value of 3, the y is at 2. This means that the slope is 2/3. And it makes sense! When we were looking at that value of 1, the y-value was less than one and looked like it was at about 2/3, or 0.666....

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Therefore, the equation is y=2/3x

I hope that this helps! Have a wonderful day!

8 0
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