Integrals

The integration of log(sin x) from 0 to pi/2 is -π/2 log2. In this section, we will find the integral of log sinx from 0 to pi/2. The following property will be used to calculate the integral. ${\int }_0^{a}f(x)dx={\int }_0^{a}f(a-x)dx$ …(i) Integral of log(sin x) from 0 to pi/2 Question: Show that $\int_0^{\frac{\pi}{2}} \log \sin x dx … Read more

Introduction to Integral Calculus: In Differential Calculus, we have learned how to find the derivative/differential of a differentiable function. The study of the inverse method of differential calculus is the main purpose of integral Calculus. We now understand this with an example. Let f(x) be a function with $f^{\prime }(x)=\frac{d}{dx}$(f(x)) = 3×2. From this information, can … Read more

Integration by Substitution Method: Some Important Forms with Examples Let f(x)  be an integrable function in one variable x. If we have to integrate some well-known twisted form of f(x),  then we may take the help of the substitution method. Here we list some important forms. Form 1: $\int f(ax+b)dx$ can be solved by the … Read more

The following topics of Integral Calculus will be covered. Please click on the link provided below you wish to read. An Introduction to Integral Calculus Integration: Definition, Properties and Formulas Proofs of all integration formulas (to be updated) Integration by substitution Integration by parts (to be updated) Integration of some special functions (to be updated) Properties of definite … Read more

List of all Integral formulas | Special Integration Formula | Integration formulas with examples —————————————————————-   Some Basic Integration Formulas    1.    $\int dx=x+c$ 2.    $\int x^{n}dx=\frac{x^{n+1}}{n+1}+c;(n\ne -1)$ 3.    $\int e^{x}dx=e^x+c$ 4.    $\int a^{x}dx=\frac{a^x}{\log |a|}+c;(a>0$ but $a\ne 1)$ 5.    $\int \frac{1}{x}dx=\log x+c$ 6.    $\int \frac{dx}{\sqrt{1-x^2}}={\sin }^{-1}x+c$ 7.    $\int \frac{dx}{1+x^2}=\tan^{-1} … Read more

Here we solve few problems of definite integrals. Problem 1:  By the definition of definite integrals, find `int_a^b dx`. Solution: From the definition of definite integrals, we have `int_a^b dx=lim_{h to 0} h sum_{1}^{n} 1, quad` where ` nh=b-a`             `=lim_{h to 0} h (1+1+1+ cdots text{till} n text{-terms})`             `=lim_{h … Read more