PROGRAMS

2015-02-18T21:22:00.001+05:30

PROGRAM 1. : PRINTING A STRING

#include<iostream>        //include header file

using namespace std;
int main()
{
    cout << "Hi friends, what's up? \n";        //comment

    return 0;
}                            //end of example

---------------------------------------------------------------
OUTPUT:

Hi friends,what's up?HitLeap - #
---------------------------------------------------------------

PROGRAM 2. : AVERAGE OF TWO NUMBERS

#include<iostream>

using namespace std;

int main()

{

float number1, number2, sum, average;

cout << "Enter two numbers: "; //prompt

cin >> number1; //read numbers

cin >> number2; //from keyboard

sum = number1 + number2;

average = sum/2;

cout << "Sum = " << sum << "\n";

cout << "Average = " << average << "\n";

return 0;

}

---------------------------------------------------------------

OUTPUT:

Enter two numbers: 1.2 2.4

sum = 3.6

average = 1.8

---------------------------------------------------------------

PROGRAM 3. : USE OF CLASS

#include<iostream>
using namespace std;
class batsman
{
    char name[40];
    int age;

    public:
        void getdata(void);
        void display(void);
};

void batsman :: getdata(void)
{
    cout << "Enter name: ";
    cin >> name;
    cout << "Enter age";
    cin >> age;
}

void batsman :: display(void)
{
    cout << "\nName: " << name;
    cout << "\nAge: " << age;
}

int main()
{
    batsman b;
    b.getdata();
    b.display();

    return 0;
}

----------------------------------------------------------
OUTPUT:
Enter name: Dhoni
Enter age: 31

Name: Dhoni
Age: 31
----------------------------------------------------------

PROGRAM 4. : SCOPE RESOLUTION OPERATOR

#include<iostream>
using namespace std;

int m = 30;       //global m

int main()
{
   int m = 40;       //m redeclared, local to main

   {
       int k = m;
       int m = 50;   //m declared again
               //local to inner block
       cout << "we are in inner block \n";
       cout << "k = " << k << "\n";
       cout << "m = " << m << "\n";
       cout << "::m = " << ::m << "\n";
   }

   cout << "\nWe are in outer block \n";
   cout << "m = " << m << "\n";
   cout << "::m = " << ::m << "\n";

   return 0;
}

-----------------------------------------------------------------
OUTPUT:
We are in inner block
k = 40
m = 50
::m = 30

We are in outer in block
m = 40
::m = 30
----------------------------------------------------------------

PROGRAM 4. : USE OF NEW AND DELETE OPERATORS

#include<iostream>
#include<conio.h>

using namespace std;

void main()
{
   int *arr;
   int size;

   cout<<"Enter the size of integer array: ";
   cin>>size;

   cout<<"Creating an array of size "<<size<<"....";
   arr = new int[size];

   cout<<"\nDynamic allocation of memory for array arr is successful. ";

   delete arr;
   getch();

}

-----------------------------------------------------------------------------
OUTPUT:
Enter the size of the integer array: 10
Creating an array of size 10....
Dynamic allocation of memeory for array arr is successful
-----------------------------------------------------------------------------

MATHS FORMULAE

2014-12-22T07:24:00.001+05:30

MATHEMATICAL FORMULAE

CALCULUS

DIFFERENTIALINTEGRAL

[A]

1. d/dx(c)=0,c=constant

2. d/dx(x^n+1/n+1)=x^n

3. d/dx(x)=1

4. d/dx(sqrt(x))=1/(2*sqrt(x))

5. d/dx(1/x)= -1/x^2

1. int{(0)dx}=c

2. int {(x^n)dx}= x^n+1/n+1 + c (n != -1)

3. int{(1)dx}=x+c

4. int{(1/(2*sqrt(x))dx}=sqrt(x)+c

5. int{(1/x^2)dx}= -1/x +c

[B]

1. d/dx(sinx) = cosx

2. d/dx(cosx) = -sinx

3. d/dx(tanx) = secx^2

4. d/dx(cotx) = -cosecx^2

5. d/dx(secx) = secx*tanx

6. d/dx(cosecx) = -cosecx*cotx

1. int{(cosx)dx} = sinx + c

2. int{(sinx)dx} = -cosx + c

3. int{(secx^2)dx} = tanx + c

4. int{(cosecx^2)dx} = -cotx + c

5. int{(secx*tanx)dx} = secx + c

6. int{(cosecx*cotx)dx} = -cosecx + c

[c]

1. d/dx(sinx^-1)= 1/(sqrt(1-(x^2)))

2. d/dx(cosx^-1)= -1/(sqrt(1-(x^2)))

3. d/dx(tanx^-1)= 1/(1+(x^2))

4. d/dx(cotx^-1)= -1/(1+(x^2))

5. d/dx(secx^-1)= 1/(x(sqrt((x^2)-1)))

6. d/dx(cosecx^-1)= -1/(x(sqrt((x^2)-1)))

1. int{(1/(sqrt(1-(x^2))))dx}= sinx^-1 + c

2. int{(1/(sqrt(1-(x^2))))dx}= -cosx^-1 + c

3. int{(1/(1+(x^2)))dx}= tanx^-1 + c

4. int{(1/(1+(x^2)))dx}= -cotx^-1 + c

5. int{(1/(x(sqrt((x^2)-1))))dx}= secx^-1 + c

6. int{(1/(x(sqrt((x^2)-1))))dx}= -cosecx^-1 + c

[D]

1. d/dx(e^x)= e^x

2. d/dx(a^x)= a^x*loga

3. d/dx(logx)= 1/x

4. d/dx(a^kx)= a^kx*k*loga

5. d/dx(e^(ax+b))= a*e^(ax+b)

6. d/dx(log(ax+b))= a/(ax+b)

7. d/dx((ax+b)^n+1)= a*(n+1)*(ax+b)^n

1. int{(e^x)dx}= e^x + c

2. int{(a^x)dx}= a^x/loga + c

3. int{(1/x)dx}= logx + c

4. int{(a^kx)dx}= a^kx/(k*loga) + c

5. int{(e^(ax+b))dx}= e^(ax+b)/a + c

6. int{(1/(ax+b))dx}= log(ax+b)/a + c

7. int{(ax+b)^n}= (ax+b)^n+1/(a*(n+1)) + c

[E]

1. d/dx(sin(ax+b))= a*cos(ax+b)

2. d/dx(sin(ax-b))= a*cos(ax-b)

3. d/dx(cos(ax+b))= -a*sin(ax+b)

4. d/dx(cos(ax-b))= -a*sin(ax-b)

5. d/dx(tan(ax+b))= a*sec(ax+b)^2

6. d/dx(tan(ax-b))= a*sec(ax-b)^2

7. d/dx(cot(ax+b))= -a*cosec(ax+b)^2

8. d/dx(cot(ax-b))= -a*cosec(ax+b)^2

1. int{(cos(ax+b))dx}= sin(ax+b)/a + c

2. int{(cos(ax-b))dx}= sin(ax-b)/a + c

3. int{(sin(ax+b))dx}= -cos(ax+b)/a + c

4. int{(sin(ax-b))dx}= -cos(ax-b)/a + c

5. int{(sec(ax+b)^2)dx}= tan(ax+b)/a + c

6. int{(sec(ax-b)^2)dx}= tan(ax-b)/a + c

7. int{(cosec(ax+b)^2)dx}= -cot(ax+b)/a + c

8. int{(cosec(ax-b)^2)dx}= -cot(ax-b)/a + c

[F]

1. d/dx[(1/a)*tan(x/a)^-1]= 1/(x^2 + a^2)

2. d/dx[(sin(x/a)^-1)]= 1/(sqrt(a^2 - x^2))

3. d/dx[log(x+(sqrt(x^2 + a^2)))]= 1/(sqrt(x^2 + a^2))

4. d/dx[log(x*sqrt(x^2 - a^2))]= 1/(sqrt(x^2 - a^2))

5. d/dx[(1/2a)*(log(x-a/x+a)]= 1/(x^2 - a^2)

6. d/dx[(1/2a)*(log(a+x/a-x)]= 1/(a^2 - x^2)

7. d/dx[(1/a)*sec(x/a)^-1]= 1/(x*sqrt(x^2 - a^2))

1. int{(1/(x^2 + a^2))dx}= (1/a)*tan(x/a)^-1 + c

2. int{(1/(sqrt (a^2 - x^2)))dx}= sin(x/a)^-1 + c

3. int{(1/(sqrt(x^2 + a^2)))dx}= log(x+sqrt(x^2 + a^2)) + c

4. int{(1/(sqrt(x^2 - a^2)))dx}= log(x+sqrt(x^2 - a^2)) + c

5. int{(1/(x^2 - a^2))dx}= (1/2a)*log(x-a/x+a) + c

6. int{(1/(a^2 - x^2))dx}= (1/2a)*log(a+x/a-x) + c

7. int{(1/(x*sqrt(x^2 - a^2)))dx}= (1/a)*sec(x/a)^-1

[G]

1. int{(secx)dx}= log(secx + tanx) + c

2. int{(cotx)dx}= log(sinx) +c

3. int{(cosecx)dx}= log(cosecx - cotx) + c

4. int{(tanx)dx}= log(secx) + c

[H]

1. d/dx(u.v)= u*(dv/dx) + v*(du/dx)

2. d/dx(u/v) = (v*(du/dx) - u*(dv/dx))/v^2

3. Integration by part:

int{(u*v)dx}= u(int{(v)dx} - int[du/dx(int{(v)dx})]dx

NOTE: To solve integration by part remember the word "LIATE" processing from L to E gradually.

where L = for Logarithmoc function; I = for Inverse trignometric function;

A = for Algebraic function; T = for Trignometric function;

E = for exponential function

SPECIAL DERIVATIVES

CHAIN RULE: If 'f' is function of 'u' and 'u' is function of 'x' then

dy/dx = (dy/du)*(du/dx) or dy/dx = (dy/du)/(dx/du)

NOTE: (i) Differential co-efficent of those trignometrical ratios which begin with 'Co' are negative

(ii) Never forget to multiply by differential co-efficient of 'u'.

Free Learning

PROGRAMS

PROGRAM 1. : PRINTING A STRING

#include<iostream> //include header fileusing namespace std;int main(){ cout << "Hi friends, what's up? \n"; //comment return 0;} //end of example

---------------------------------------------------------------OUTPUT:Hi friends,what's up?HitLeap - #---------------------------------------------------------------

PROGRAM 2. : AVERAGE OF TWO NUMBERS

#include<iostream>

using namespace std;

int main()

{

float number1, number2, sum, average;

cout << "Enter two numbers: "; //prompt

cin >> number1; //read numbers

cin >> number2; //from keyboard

sum = number1 + number2;

average = sum/2;

cout << "Sum = " << sum << "\n";

cout << "Average = " << average << "\n";

return 0;

}

---------------------------------------------------------------

OUTPUT:

Enter two numbers: 1.2 2.4

sum = 3.6

average = 1.8

---------------------------------------------------------------

PROGRAM 3. : USE OF CLASS

PROGRAM 4. : SCOPE RESOLUTION OPERATOR

PROGRAM 4. : USE OF NEW AND DELETE OPERATORS

MATHS FORMULAE

#include<iostream> //include header file

using namespace std;
int main()
{
cout << "Hi friends, what's up? \n"; //comment

return 0;
} //end of example

---------------------------------------------------------------
OUTPUT:

Hi friends,what's up?HitLeap - #
---------------------------------------------------------------