Math Doubts

Integral of sinx formula

Fact-checked:

Formula

$\displaystyle \int{\sin{x}}\,dx$ $\,=\,$ $-\cos{x}+c$

What is the Integral of Sine?

The integral of sine $x$ with respect to $x$ is equal to negative cosine $x$ plus a constant of integration.

The integral of sine is the antiderivative of the trigonometric function $\sin{x}$ with respect to $x$. It represents the function whose derivative is $\sin{x}$.

$\displaystyle \int{\sin{x}}\,dx$

The integral of $\sin{x}$ can be evaluated directly, and the result is $−\cos{x}$ plus a constant of integration.

$\displaystyle \int{\sin{x}}\,dx$ $\,=\,$ $-\cos{x}+c$

Common Mistakes in Integrating sin x

When integrating $\sin{x}$, students often make two common mistakes.

  1. Forgetting the minus sign before the $\cos{x}$ function.
  2. Neglecting the constant of integration.

Recognizing these mistakes helps you avoid errors, solve problems correctly, and build a stronger understanding of the integral of $\sin{x}$.

Importance of the Integral of sin x

There are five strong reasons why every student must learn the integration of the sine function.

  1. Builds a clear understanding of antiderivatives and indefinite integrals.
  2. Useful as a base formula for solving more complex trigonometric integrals.
  3. Required for applications involving differential equations and integral calculus.
  4. Strengthens the connection between differentiation and integration.
  5. Frequently appears in exams, textbooks, and competitive mathematics problems.
Ashok Kumar B.E. - Founder of Math Doubts

Ashok Kumar, B.E.

Founder of Math Doubts

A Specialist in Mathematics, Physics, and Engineering with 14 years of experience helping students master complex concepts from basics to advanced levels with clarity and precision.

Story of Math Doubts

Proof of the Integral of Sine

Explore the step-by-step derivation of the integral of sine, ∫sin x dx, to see why it equals −cos x plus the constant of integration.

Proof of Sine Integral