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Serga [27]
3 years ago
6

In the diagram shown,

Mathematics
1 answer:
STALIN [3.7K]3 years ago
4 0
The answer that you are looking for is D
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How do you integrate arctan(x dx? i think that if you simplify the integral you get:?
Temka [501]
Integration by parts will help here. Letting u=\arctan x and \mathrm dv=\mathrm dx, you end up with \mathrm du=\dfrac{\mathrm dx}{1+x^2} and v=x. Now

\displaystyle\int\arctan x\,\mathrm dx=uv-\int v\,\mathrm du
\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\int\frac x{1+x^2}\,\mathrm dx

For the remaining integral, setting y=1+x^2 gives \dfrac{\mathrm dy}2=x\,\mathrm dx, so

\displaystyle\int\frac x{1+x^2}\,\mathrm dx=\frac12\int\frac{\mathrm dy}y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C

Putting everything together, you end up with

\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\frac12\ln(1+x^2)+C
6 0
3 years ago
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find the length of AC.
Oxana [17]

Answer:

AC=16 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.  It was given that diagonals AC and BD intersect at point E.

This implies that: AE=CE.

We substitute the expression for x, we get:

11x-3=12-4x.

Group similar terms to get:

11x+4x=12+3.

15x=15.

x=1

AC = 2(12-4x)

AC=2(12-4(1))

AC=2(8)

AC=16

8 0
3 years ago
girls in the first grade account for one-third of the total strength of the class 3 girls are absent today. find the total stren
BabaBlast [244]
1/3x-3= 4;21 students
7 0
3 years ago
If f(x) = 12 – 2 and g(x) = x + 3, find all values of x, to the nearest tenth, for
Leto [7]

Answer:

x=7

Step-by-step explanation:

f(x) =g(x)

12-2=x+3

10=x+3

10-3=x

x=7

6 0
3 years ago
Write 12.6 as a mixed number with the fraction in simplest form
Naily [24]
Using your knowledge of place value the number is

12 6/10 which then reduces to

12 3/5
6 0
2 years ago
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