Math Problem Statement
integral sin(4x)dx
Solution
The integral of with respect to can be solved using basic integration rules. Here's the solution:
To solve this, we use substitution. Let:
Now substitute into the integral:
Factor out the constant :
The integral of is , so:
Substitute back into the equation:
Thus, the integral is:
Would you like more details on the steps or have any questions?
Here are 5 related questions:
- How do you integrate functions with other trigonometric identities, such as ?
- What is the integral of a product of sine and cosine, such as ?
- Can substitution be used to solve integrals of higher powers of trigonometric functions?
- What is the derivative of ?
- How does the integral of compare to , where is a constant?
Tip: Always look for substitutions in integrals involving complex trigonometric functions; it often simplifies the process significantly.
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Math Problem Analysis
Mathematical Concepts
Calculus
Trigonometric Integration
Substitution
Formulas
∫sin(kx) dx = -(1/k) cos(kx) + C
Substitution: u = 4x, du = 4 dx
Theorems
Basic Integration Rules
Suitable Grade Level
Grades 11-12, College
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