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uranmaximum [27]
3 years ago
14

\int (x+1)\sqrt(2x-1)dx

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
6 0

Answer:

\int (x+ 1) \sqrt{2x-1} dx =  \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C

Step-by-step explanation:

\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v =  \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}

\int (x+1)\sqrt(2x-1)dx\\\\   = uv - \int v du                              

= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  [ \ u = x + 1 => du = dx  \ ]    

= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\=  \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\

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a car travels along the highway to yuma at steady speed. when it begins, it is 400 miles from yuma. After 7 hours, it is 59 mile
klemol [59]

Answer:

y= -50x + 400

Step-by-step explanation:

-50 miles from the place which means they are going further and further away so it is negative. And its 400 because y=mx+b the b is 400 because thats where they started.  Also it said it was correct on A-p-e-x.

4 0
3 years ago
Simplify this expression and show all steps:<br> 48m^7/20m^4
Ghella [55]

Answer:

(12/5)m^3

Step-by-step explanation:

It's easier for most of us to write out a fraction / ratio without the " / " symbol:

48m^7

------------

20 m^4

Separate the coefficients from the powers of m:

48     m^7

----- * --------     Now let's reduce each fraction separately:

20      m^4


48/20 = 12/5, and

(m^7) / (m^4) = m^(7-4) = m^3


... so that our final answer is (12/5)m^3.

3 0
2 years ago
What is the perimeter of a rectangle with sides 2/3x+10 and 1/3x+5
gogolik [260]

Answer:

The perimeter of the rectangle  is 2x+ 30

Step-by-step explanation:

Sides of the rectangle are 2/3x+10 and 1/3x+5

Now, Perimeter of the Rectangle = 2(Length + Breadth)

Here, sum of the sides = (\frac{2}{3}x + 10 )  + (\frac{1}{3}x + 5 )  = (\frac{2}{3}x +\frac{1}{3}x  )  + ( 10+ 5 )

adding like terms with like terms, we get

(\frac{2x + x}{3})  + 15 = \frac{3x}{3}  + 15

Hence, Sum = (x + 15)

Now,  2(Length + Breadth)  = 2(x+15) = 2x + 30

hence, the perimeter of the rectangle  = 2x+ 30

8 0
3 years ago
PLEASE HELP!! Question with picture is below
Alenkinab [10]

Answer:

It honestly does not matter, but I'd choose the ring because I feel like it is more pleasant to look at.  

Step-by-step explanation:

We need to find the area of both shapes to compare:

3/4 of a circle:

A = 6^2pi

= 36pi

36pi(0.75) = 27pi

Ring:

A = 36pi

A2 = 3^2pi = 9pi

36pi-9pi = 27pi

As you can see, the two areas are the same.

Hope this helped! :)

8 0
3 years ago
Read 2 more answers
Help? Fraction? Triangle similarity.<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B62%7D%7B15.5%7D%20x%20%20%5Cfrac%7B92%7D%7Bx%
Over [174]
62 / 15.5  = 92 /  x

to find x cross multiply:-

62x = 15.5 * 92
x =  (15.5*92) / 62
  = 23
8 0
3 years ago
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