Math Problem Statement

intergrate sin x dx 

Solution

The integral of sin(x)\sin(x) with respect to xx is a standard result in calculus. To compute it, we use basic integration rules.

sin(x)dx=cos(x)+C\int \sin(x) \, dx = -\cos(x) + C

where CC is the constant of integration.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. How do you integrate cos(x)\cos(x)?
  2. What is the integral of sin(kx)\sin(kx) where kk is a constant?
  3. How do you differentiate sin(x)\sin(x)?
  4. Can you solve sin2(x)dx\int \sin^2(x) \, dx?
  5. How does the constant of integration, CC, affect the final solution?

Tip: Always remember that the constant of integration is crucial when solving indefinite integrals.

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometric Functions
Indefinite Integration

Formulas

∫ sin(x) dx = -cos(x) + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12