Integrate indefinite integral:
Solution:
1. use substitution
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2. decompose into partial fractions
where A=1/2, B=1/2, C=-1
3. Substitute partial fractions and continue
4. back-substitute u=e^x
Note: log(x) stands for natural log, and NOT log10(x)
Answer:
x<4
Step-by-step explanation:
To solve for x in the inequality equation, the terms should be rearranged such that x is on one side and integers are on the other side.
First, expand 4(x-3).
This will obtain:
Now, shift x terms and integers on each side.
After simplifying, it will get:
Finally, we can solve for x.
We can also draw the respective graph (please don't mind my drawings), where the area shaded in green is the range.
Step-by-step explanation:
√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))
Square and take the square root.
√[√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))]²
√[(1 + sin x) / (1 − sin x) + 2 + (1 − sin x) / (1 + sin x)]
Add the fractions using least common denominator.
√[((1 + sin x)² + (1 − sin x)²) / (1 − sin²x) + 2]
√[(1 + 2 sin x + sin²x + 1 − 2 sin x + sin²x) / (1 − sin²x) + 2]
√[(2 + 2 sin²x) / (1 − sin²x) + 2]
Use Pythagorean identity:
√[(2 + 2 sin²x) / (cos²x) + 2]
√[2 sec²x + 2 tan²x + 2]
√[2 sec²x + 2 (tan²x + 1)]
Use Pythagorean identity:
√[2 sec²x + 2 sec²x]
√[4 sec²x]
±2 sec x
If x is in the second quadrant, then sec x < 0.
-2 sec x
Answer:
Amaya is wrong.
Step-by-step explanation:
The perimeter of the square is 20 inches, which means each side of the square needs to add up to 20 inches. If the side length of that side Amaya pointed out is 4 inches, then the total perimeter would only be 18 inches, in another case, if they were talking about the area of the square/rectangle (now), it would be 20 inches. So, Amaya is wrong.
