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Gemiola [76]
2 years ago
6

Complete the square and give a substitution (not necessarily trigonometric) which could be used to compute the integral. ∫1x2+2x

+2dx
Mathematics
1 answer:
Ugo [173]2 years ago
5 0

Answer:

Substitution of x+1

Step-by-step explanation:

We are given that

\int \frac{1}{x^2+2x+2}dx

\int\frac{1}{(x^2+2x+1)+1}dx

\int\frac{1}{(x+1)^2+1^2}dx

By using identity

(a+b)^2=a^2+b^2+2ab

Substitute x+1=t

Differentiate w.r.t x

dx=dt

Substitute the values

\int\frac{1}{t^2+1^2}dx

\frac{1}{1}tan^{-1}\frac{t}{1}+C

By using formula :\int\frac{1}{x^2+a^2}dx=\frac{1}{a}tan^{-1}\frac{x}{a}+C

tan^{-1}(x+1)+C

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1. 7:4 = 21:x; what is the value of x?<br> A. 12<br> B. 10<br> C. 8<br> D. 6<br> E. 4<br> 8.
Soloha48 [4]

Answer:

x = 12

I hope it's helps you

8 0
2 years ago
The diagram above shows a rectangle inscribed in a circle AB=10 and AC =12 caculate the total surface area of the shaded part
erastova [34]

Answer:

71.63 \: \: \mathrm{cm^2 }

Step-by-step explanation:

Once we know the diameter of the circle, we can figure out the problem.

The diameter of the circle = The diagonal of the rectangle inscribed in the circle

To find the diagonal of the rectangle, we can use a formula.

d=\sqrt{w^2 + l^2}

The width is 10 cm and the length is 12 cm.

d=\sqrt{10^2 + 12^2}

d \approx 15.62

The diagonal of the rectangle inscribed in the circle is 15.62 cm.

The diameter of the circle is 15.62 cm.

Find the area of the whole circle.

A=\pi r^2

The r is the radius of the circle, to find radius from diameter we can divide the value by 2.

r = \frac{d}{2}

r=\frac{15.62}{2}

r=7.81

Let’s find the area now.

A=\pi (7.81)^2

A \approx 191.625

Find the area of rectangle.

A=lw

Length × Width.

A = 12 \times 10

A=120

Subtract the area of the whole circle with the area of rectangle to find area of shaded part.

191.625-120

71.625 \approx 71.63

5 0
2 years ago
Urgent!!!!!!!plzz
Nitella [24]

Answer:

too much reading, can you put more points.

(edit: OML SO SORRY -THOUGHT THIS WAS QUESTIONS)

Step-by-step explanation:

7 0
3 years ago
PLEASE HELP ME<br> QUICK PLEEEEAAASE
sasho [114]

Answer:

A 2/6 and 3/6 is the Answer

7 0
3 years ago
Read 2 more answers
Please help find surface area!!
NeTakaya

Answer:

138 cm.

Step-by-step explanation:

So first, we find the S.A. of the front and back.

The diagram says the side length of the front is 3 cm. and 3 cm.

3x3=9. So then, the back is also 9 cm, 9+9=18.

Now to find the S.A.'s of the four sides, you have to see the side lengths of each of them. The side lengths are 3 and 10.

3x10=30. This means each of them is 30 cm.

30x4=120. 120 is the total surface area of the four sides.

To find the total surface area of the whole rectangle, you add all the surface areas.

120+18=138 cm. (Not squared, since it's surface area and not area.)

3 0
3 years ago
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