More Examples of Integration
Example: Solution: We have
Example: Solution: We have
Evaluate (i) (ii) Solution: (i) (ii)
1) 2) Where is any constant. 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) or 18) 19) or 20) or 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) or 36) or 37) or 38) or 39) or 40)
The inverse process of derivatives called anti–derivatives or integration. “A function being given and it is required to find a Second function whose derivative with respect to x, is, that is, Thus if Then The function , then, is called the anti-derivate or indefinite integral of . Symbol of Integration: The function is called integrand […]
In this tutorial we shall solve a differential equation of the form , by using separating the variables method. Given differential equation of the form This differential equation also be written as Separating the variables, the given differential equation can be written as Keep in mind that in separating variable technique the terms and are […]
In the following example we shall discuss application of simple differential equation in business. If is the principal amount and is the rate of interest, then the differential equation relating the time , and is Example: How long will it take for Rs.10000 to double itself if it is compounded continuously at 4 percent annum? […]
Differential equations are commonly physical problems. In the following example we shall discuss a very simple application of ordinary differential equation in physics. Example: A ball is thrown vertically upward with a velocity of 50m/sec. Neglecting air resistance, find (i) Velocity of ball at any time (ii) Distance travelled in any time (iii) Maximum height […]
Differential equations are frequently used in solving the mathematical and physical problems. In the following example we shall discuss application of simple differential equation in biological sciences. Example: In a culture bacteria increases at the rate proportional to the number of bacteria present. If bacteria are 400 initially and are doubled in 3 hours, find […]
In this tutorial we shall solve a differential equation of the form , by using separating the variables method. Given differential equation of the form This differential equation also be written as Separating the variables, the given differential equation can be written as Keep in mind that in separating variable technique the terms and are […]
In this tutorial we shall solve a differential equation of the form , by using separating the variables method. Given differential equation of the form This differential equation also be written as Separating the variables, the given differential equation can be written as Keep in mind that in separating variable technique the terms and are […]
In this tutorial we shall solve a differential equation of the form , by using separating the variables method. Given differential equation of the form This differential equation also be written as Separating the variables, the given differential equation can be written as Keep in mind that in separating variable technique the terms and are […]
In this tutorial we shall solve a differential equation of the form , by using separating the variables method. Given differential equation of the form This differential equation also be written as Separating the variables, the given differential equation can be written as Keep in mind that in separating variable technique the terms and are […]