What are integrals and derivatives?

What are integrals and derivatives?

Derivative is the result of the process differentiation, while integral is the result of the process integration. • Derivative of a function represent the slope of the curve at any given point, while integral represent the area under the curve.

What are the integrals of the 6 trigonometric functions?

Integrals of Trigonometric Functions

Function Integral
cos2x x/2 + sin(2x)/4 + c = (x + sinx ∙ cosx)/2 + c
tanx = sec2x -ln|cosx| + c
cotx = -csc2x ln|sinx| + c
secx ln|secx + tanx| + c

What are trig integrals?

In this section we look at how to integrate a variety of products of trigonometric functions. These integrals are called trigonometric integrals. They are an important part of the integration technique called trigonometric substitution, which is featured in Trigonometric Substitution.

Why do we need trig identities?

Trig identities are trigonometry equations that are always true, and they’re often used to solve trigonometry and geometry problems and understand various mathematical properties. Knowing key trig identities helps you remember and understand important mathematical principles and solve numerous math problems.

What are integrals used for?

An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects. Therefore, finding the integral of a function with respect to x means finding the area to the X-axis from the curve.

Why are integrals so important?

The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.

How do you integrate sin2x?

Integration of Sin2x

  1. Integration of sin2x means finding the integral of the function sin2x.
  2. The formula for the integral of sin 2x dx is given by:
  3. We can derive the formula of integral of sin2x using the method of integration by substitution.
  4. Consider ∫sin2x dx.
  5. Let u = 2x such that du = 2dx ⇒ dx = (½)du.