**Level:** F.Sc (Pre-Engg)**Class:** 2nd Year**Board:** Punjab Textbook Board**Subject:** Mathematics**Total Exercises:** 8**Type:** Notes

TITLE | SOLUTION |
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Exercise 3.1 | View |

Exercise 3.2 | View |

Exercise 3.3 | View |

Exercise 3.4 | View |

Exercise 3.5 | View |

Exercise 3.6 | View |

Exercise 3.7 | View |

Exercise 3.8 | View |

**In this chapter we will read these topics:**

- What is the differential of a function f(x) and what is the differential coefficient?
- What is the difference between delta(y) and dy?
- Use differential to find approximate value.
- Find the approximate increase in the volume of a cube of the length its each edge changes from 5 to 5.02.
- Find the approximate increase in the area of a circular disc if its diameter is increased from 44com to 44.4.
- Define integration.
- Some basic tips for integration.
- Define the indefinite integral.
- Write two theorems on anti-derivatives.
- Some basic formulae.
- Evaluate the problems.
- Write a note on integration by substitution.
- Write some important trigonometric substitutions.
- Integration by parts.
- Integration by partial fractions.
- When denominator contains non-repeated linear factors.
- When denominator contains repeated linear factors.
- When denominator contains non-repeated irreducible quadratic factors.
- Define definite integral.
- Define the fundamental theorem of integral calculus.
- Area under the curve.
- Find the area bounded by the curve.
- Find the area between the x-axis and the curve.
- Define the differential equations.
- Define the order of a differential equation.
- Define the degree of a differential equation.
- Define solution of a differential equation.
- Define general solution of a differential eqaution.
- Define particular solution of a differential equation.
- How many constants are involved in general solution of first-order differential equation.
- How many constants are involved in general solution of nth order.
- Solve the following differential equations.