Integration by parts
In words: Integral of the product of two functions If the integrand is the product of two functions of different types then their order is determined by the word ILATE where I = Inverse trigonometric L = Logarithmic A = Algebraic, T = Trigonometric, E = Expone..
In words: Integral of the product of two functions If the integrand is the product of two functions of different types then their order is determined by the word ILATE where I = Inverse trigonometric L = Logarithmic A = Algebraic, T = Trigonometric, E = Expone..Integration by Parts
Let u and v be two differentiable function of a single independent variable x. Integrating w.r.t x on both sides Let u = f(x), Then \ (1) can be written ..
Let u and v be two differentiable function of a single independent variable x. Integrating w.r.t x on both sides Let u = f(x), Then \ (1) can be written ..Standard integrals
By method of completing squares ax 2 + bx + c is expressed as A 2 + X 2 or X 2 - A 2 and the integral reduces to which can be evaluated using the standard integrals..
By method of completing squares ax 2 + bx + c is expressed as A 2 + X 2 or X 2 - A 2 and the integral reduces to which can be evaluated using the standard integrals..Indefinite Integrals as Antiderivative (Contd...)
Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent. Comparison between differentiation and integration: 1. The derivative of a function, when it exists is a unique function. The integral..
Some Special Types of Integrals
Prove that The quadratic expression ax 2 + bx + c can be expressed in the form a(x 2 A 2 ) by the method of completing the square. The integrals can be evaluated by using the special integrals..
Prove that The quadratic expression ax 2 + bx + c can be expressed in the form a(x 2 A 2 ) by the method of completing the square. The integrals can be evaluated by using the special integrals..Some Properties of Definite Integrals
The Properties of Definite Integrals are: 2) ..
The Properties of Definite Integrals are: 2) ..Definite Integral as a Limit of Sum
Let f be a continuous non-negative function defined on a closed interval [a, b]. Since the value of the function is non-negative, the graph of the function is a curve above X-axis. Let the graph of the curve be as shown in the figure.Let f be a continuous non-negative function defined on a closed i..
Let f be a continuous non-negative function defined on a closed interval [a, b]. Since the value of the function is non-negative, the graph of the function is a curve above X-axis. Let the graph of the curve be as shown in the figure.Let f be a continuous non-negative function defined on a closed i..Comparison between differentiation and integration
1. Both are operations on functions. 2. Both are linear. This is because of the following: (i) (ii) The constant can be taken outside the differential as well as integral sign as shown below: 3. We heve already seen that not all functions are differentiable. Similarly, all funct..
1. Both are operations on functions. 2. Both are linear. This is because of the following: (i) (ii) The constant can be taken outside the differential as well as integral sign as shown below: 3. We heve already seen that not all functions are differentiable. Similarly, all funct..Definite Integrals Animation
Definite Integrals Animation..
Definite Integrals Animation..See what our Users say :
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