Integral calculus formula

Integral calculus the the reverse process of differentiation. So if differentiation of f(x) is g(x) then f(x) is called the integral or anti-derivative of g(x). It is written as $\int g(x)dx = f(x)$

If $\frac{d}{dx}f(x) = g(x)$, $\frac{d}{dx}f(x) + C = g(x)$ where C is any constant. Thus, if f(x) is the integral of g(x) then f(x)+1 or f(x)+5 or in general f(x)+C is also an integral of g(x). So, based on this fact we write $\int g(x)dx = f(x)+C$ where C is any constant.

INTEGRAL PROPERTIES
$\int Cf(x)dx = C \int f(x)dx$
$\int {f_1(x) \pm f_2(x)} dx = \int f_1(x) dx \pm \int f_2(x) dx$

View On WordPress

1. Type in “Google in 1998″ for using the very old version of the search engine.

2. To Look for the meaning and etymology of any word just type “proactive etymology”

3. To play a hidden game built in the Google search engine just enter “Zerg Rush”

4. Just enter “Festivus” on search box and see what happens. Let me know on comment what happened.

5. Type “define anagram” and see how geeky Google…

View On WordPress

Elastic collision in one dimension

Elastic collision in one dimension

Any collision is elastic if the total kinetic energy of the colliding particles remains conserved. Let us consider two bodies A and B with masses $m_1$ and $m_2$ are moving with the initial velocity $u_1$ and $u_2$ respectively in the same direction and same straight line. In this problem let us suppose that velocity of one object is greater than other $(u_1 > u_2)$and they are on the collision path. In this situation object A…

View On WordPress

Projectile motion in Horizontal direction

Projectile motion in Horizontal direction

Let us suppose that an object is thrown from a certain height ‘h’ above the ground in horizontal direction with initial velocity ‘u’. This horizontal velocity remains unaffected by the acceleration due to gravity. In this case ‘g’ remains constant throughout the motion. There are two way motion in the projectile, one is vertical motion and another is horizontal motion.

Vertical motion
Just after…

View On WordPress

Quantum Computers

A classical computer performs operations using classical bits which can be either 0 or 1. Now in contrast a quantum computer uses quantum bits or qubits and they can be both 0 & 1 at the same time and it is this that gives a quantum computer its superior computing power. There are a number of physical objects that can be used as a qubit, a single photon a nucleus or an electron. Researchers are…

View On WordPress

2014 FIFA World Cup match schedule and results

2014 FIFA World Cup match schedule and results

2014 FIFA world cup will be the 20th football world cup which is taking place in Brazil from 12 June to 13 July 2014. Brazil is hosting the FIFA world cup for the second time the first one was held in 1950. There will be altogether 64 matches played around 12 cities. Spain is the defending champions. There are altogether 32 nations fighting for the title. The competing nations for 2014 FIFA world…

View On WordPress

One Plus one

We are talking about a phone a phone (one plus one) that is taking the internet by storm very recently since it was announced and revealed as the one plus one. To clarify things, company name is one plus and the phone name is 1. One plus is a Chinese manufacture and are relatively new company hence we are not sure about what to expect from them but he new device have pretty good specs.

The real…

View On WordPress

Postulates of Quantum mechanics

Postulates of Quantum mechanics

Few postulates of Quantum mechanics are stated below:

Postulate 1 (describes the state of quantum mechanical system): At a given time $t_o$ the state of quantum mechanical system is defined by specifying a ket $|\psi(t_o)>$ belonging to state space $\varepsilon$.

Postulate 2 (description of physical quantity): Every measurable quantity A is described by an observable $\hat{A}$ acting in the state space $\varepsilon$.

Postulate 3 (Measurement of…

View On WordPress

What is Heartbleed bug?

What is Heartbleed bug?

Heartbleed is an open source OpenSSL cryptography library security bug. OpenSSL is used for Transport Layer Security (TLS) protocol. A patched version of OpenSSL is already released since April 7,  2014 which coincide with the public disclosure of the bug itself. The bug could potentially allow the theft of passwords, user’s session cookies and servers private keys used for encryption. Heartbleed…

View On WordPress

Escape velocity

We all know that everything thrown vertically upward will eventually fall down. When we throw an object, it moves up to a maximum height and then comes back to the surface. The maximum height attained depends on the velocity of the object. If we talk about the energy, the Kinetic Energy present in the body is used in doing work against gravity. As the body moves upward, its kinetic energy keeps…

View On WordPress