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Flauer [41]
2 years ago
5

How to evaluate the integral

Mathematics
1 answer:
Papessa [141]2 years ago
8 0
Remember
for F(x) is the antiderivitive of f(x)
\int\limits^a_b {f(x)} \, dx =F(a)-F(b)
so find the antiderivitive of ((x+1)^2)/x

if we expand we get (x^2+2x+1)/x which simplifies to x+2+(1/x)
the anti-deritivive of  x is (1/2)x^2
the antideritiveve of 2 is 2x
the antideritivieve of 1/x is ln|x|

F(x)=(1/2)x^2+2x+ln|x|+C

\int\limits^2_1 { \frac{(x+1)^2}{x} } \, dx =F(2)-F(1)

F(1)=(5/2)+ln1+C
F(2)=6+ln2+C

F(2)-F(1)=6+ln2+C-(5/2+ln1+C)
F(2)-F(1)=(7/2)+ln2
that is the answer
if you want is simplified or expanded it is about 4.1915
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Solve each equation:
omeli [17]
You sure seem to be asking a lot of questions lately. I'd like to see that you've been trying with these problems at least because if you can't get that first one it's almost like you missed the whole lesson.

1. 20 = 4b + 7 + 5
Add the 7 and 5.
20 = 4b + 12
Subtract 12 from each side.
8 = 4b
Divide each side by 4.
2 = b

2. 7 = 6k - 7k
6k - 7k = -1k. (the k acts as a sort of unit)
7 = -1k
Divide each side by -1.
-7 = k

3. 3.23 - 2m = 3 - 2(5m - 2)
Distribute the ×-2 to each term inside the parentheses.
3.23 - 2m = 3 - 10m + 4
Add the 3 and 4.
3.23 - 2m = 7 - 10m
Add 10m to each side.
3.23 + 8m = 7
Subtract 3.23 from each side.
8m = 3.77
Divide by 8.
m = 0.47125

4. -88/45=1/3r+2/5r
To get rid of the fractions, let's multiply everything by 45.
-88 = 15 + 18r
Subtract 15 from each side.
-103 = 18r
Divide by 18.
-103/18 = r
As a mixed number, r = -5 and 13/18
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6 0
3 years ago
F(x)=(-3x+2) and g(x)=(2x^2-5x-1)
pashok25 [27]

Answer: -6x² + 15x + 5

Step-by-step explanation:

To solve this problem, you only need to substitute g(x)'s equation as the value of the x in f(x), then simplify.

Step 1: f(x) = -3(2x² - 5x - 1) + 2

Step 2: Apply the distributive property

-3(2x²) + -3(-5x) + -3(-1)

-6x² + 15x + 3

Step 3: Simplify

f(x) = -6x² + 15x + 3 + 2

f(x) = -6x² + 15x + 5

6 0
2 years ago
Help please i will give brainlist
Feliz [49]

Answer:

Angle 1 is 67 and Angle 2 is 46

Step-by-step explanation:

5 0
3 years ago
I need help. I'm confused ​
Alex
So, it is most likely that Joel runs 7 miles a day. On the x-axis would be the number of days he runs and the y-axis would be the mileage.
4 0
2 years ago
Use decimals to express a probability in tenths.
Alisiya [41]
The answer is 1/10
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4 0
3 years ago
Read 2 more answers
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