Find the right course for you
70287 Courses
Course Detail
Back to Search ResultsOffered by:
Udemy

Duration: Lifetime Access

Course type: Online

Course starts: Any time

Course fees: US$ 399.99

Register before: Any time

Registration Fees: Free
Delivered by:
Udemy
With a mission to improve lives through learning, Udemy is the online learning destination that helps students, businesses, and governments gain the skills they need to compete in today’s economy. More than 30 million students are mastering new skills from expert instructors teaching over 100,000 online courses in topics from programming and data science to leadership and team building.
VIEW ALL COURSES
600 Harrison St.
3rd Floor San Francisco
CA 94107
United States
Applied Mathematics  Integrals & Application of Integrals
IITJEE Main & Advanced  BITSAT  SAT  MSAT  MCAT  State Board  CBSE  ICSE  IGCSE
Integrals
Integration as inverse process of differentiation
Integration of a variety of functions by substitution, by partial fractions and by parts
Evaluation of simple integrals of the following types and problems based on them
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)
Basic properties of definite integrals and evaluation of definite integrals
Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only)
Area between any of the two above said curves (the region should be clearly identifiable)
SUMMARY
Integrals
1. Integration is the inverse process of differentiation. In the differential calculus, we are given a function and we have to find the derivative or differential of this function, but in the integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation. These integrals are called indefinite integrals or general integrals, C is called constant of integration. All these integrals differ by a constant.
2. From the geometric point of view, an indefinite integral is collection of family of curves, each of which is obtained by translating one of the curves parallel to itself upwards or downwards along the yaxis.
3. Some properties of indefinite integrals are as follows:
i. ∫ [f(x) + g(x)]dx = ∫ f(x) dx + ∫ g(x) dx
ii. For any real number ∫ k f(x) dx = k ∫ f(x) dx
More generally, if f 1 , f 2 , f 3 , ... , f n are functions and k1 , k2 , ... ,kn are real numbers.
4. A change in the variable of integration often reduces an integral to one of the fundamental integrals. The method in which we change the variable to some other variable is called the method of substitution. When the integrand involves some trigonometric functions, we use some well known identities to find the integrals. Using substitution technique, we obtain the following standard integrals.
(i) ∫ tan x dx = log sec x + C (ii) ∫ cot x dx = log sin x + C
(iii) ∫ sec x dx = log sec x + tan x + C (iv) ∫ cosec x dx = log cosec x  cot x + C
Applications of the Integrals
1. The area of the region bounded by the curve y = f (x), xaxis and the lines x = a and x = b (b > a)
2. The area of the region bounded by the curve x = φ (y), yaxis and the lines y = c, y = d