Math Problem Statement

find the integral of cos x

Solution

The integral of cosx\cos x is:

cosxdx=sinx+C\int \cos x \, dx = \sin x + C

Explanation:

  • The derivative of sinx\sin x is cosx\cos x, so the antiderivative (integral) of cosx\cos x is sinx\sin x.
  • CC is the constant of integration, since this is an indefinite integral.

Would you like me to show step-by-step reasoning or apply this to a specific interval (definite integral)?

Related Questions

  1. What is the integral of cos(2x)\cos(2x)?
  2. How do you evaluate cosxdx\int \cos x \, dx from x=0x = 0 to x=πx = \pi?
  3. What is the integral of sinx\sin x?
  4. How do you solve ecosxsinxdx\int e^{\cos x} \sin x \, dx?
  5. Can you find the second derivative of sinx\sin x?

Tip

Always check if you need a definite or indefinite integral before solving—it changes the process and the result.

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Math Problem Analysis

Mathematical Concepts

Integration
Trigonometric Functions

Formulas

∫cos(x) dx = sin(x) + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12