Evaluate the integral. (use c for the constant of integration.) 8 sin2(x) cos3(x) dx
1 answer:
Important formula we will use.
First formula
2 cos α sin β = sin (α + β) - sin (α - β)
Second formula
∫ sin x dx = - cos x + c
We should change the trigonometry expression from multiplication into addition. Use the first formula above
∫ 8 sin (2x) cos (3x) dx
= ∫ 4 ( 2 sin (2x) cos (3x) dx)
= 4 ∫ 2 cos (3x) sin (2x) dx
= 4 ∫ sin (3x + 2x) - sin (3x - 2x) dx
= 4 ∫ sin 5x - sin x dx
After changing into addition, solve the integration. Use the second formula.
= 4 ∫ sin 5x - sin x dx
This is the answer.
First formula
2 cos α sin β = sin (α + β) - sin (α - β)
Second formula
∫ sin x dx = - cos x + c
We should change the trigonometry expression from multiplication into addition. Use the first formula above
∫ 8 sin (2x) cos (3x) dx
= ∫ 4 ( 2 sin (2x) cos (3x) dx)
= 4 ∫ 2 cos (3x) sin (2x) dx
= 4 ∫ sin (3x + 2x) - sin (3x - 2x) dx
= 4 ∫ sin 5x - sin x dx
After changing into addition, solve the integration. Use the second formula.
= 4 ∫ sin 5x - sin x dx
This is the answer.
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Answer:
Step-by-step explanation:
Given the following inequality:
You need to solve for "x" in order to find the solution.
The steps are:
1. Add to both sides of the inequality:
2. Add to both sides:
3. Divide both sides by :
Notice that "x" is less than 8. This indicates that 8 is not included in the solution and you must use parentheses.
The solution in Interval notation is: