Calculating Indefinite Integral
Various steps to calculate the indefinite integrals are,
- Step 1: Normal indefinite integrals are solved using direct integration formulas.
- Step 2: Integrals with rational functions are solved using the partial fractions method.
- Step 3: Indefinite integrals can be solved using the substitution method.
- Step 4: Integration by parts is used to solve the integral of the function where two functions are given as a product.
Example: Find the indefinite integral ∫ x3 cos x4 dx
Solution:
Using the substitution method.
Let us assume,
x4 = t
4x3 dx = dt
Now, ∫ x3 cos x4 dx
= 1/4∫cos t dt
= 1/4 (sin t) + C
= 1/4 sin (x4 ) + C
Integration Formulas
Indefinite Integrals: The derivatives have been really useful in almost every aspect of life. They allow for finding the rate of change of a function. Sometimes there are situations where the derivative of a function is available, and the goal is to calculate the actual function whose derivative is given.
In this article, we will discuss Indefinite Integrals, graphical interpretation, formulas, and properties.
Table of Content
- What are Indefinite Integrals?
- Graphical Interpretation of Integrals
- Integrals by Graphs
- Calculating Indefinite Integral
- All Formulas of Indefinite Integrals
- Properties of Indefinite Integrals
- Property of Sum
- Property of Difference
- Property of Constant Multiple
- Difference Between Indefinite Integral and Definite Integral
- Indefinite Integrals Examples
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