Definite Integrals
Definite Integrals - Differentiation deals with the rate of change while integration deals with the total change. The definite integrals are evaluated in problems relating to plane, areas, areas and volumes of solid of revolution etc. In this chapter, we confine oursel..
Indefinite Integrals
Introduction - Integration and differentiation are a pair of inverse operations. So far, from a given function, we have been finding its derivative but the question arises: what is the function whose derivative is known? If the derivative of a function is given, then the functio..
Integration by Substitution
If u is a function of x, we can use the following formula to evaluate an integral. f dx = (f/(du/dx)) du Using the Formula Use of the formula is equivalent to the following procedure: 1. Write u as a function of x..
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 = Exponential In the integra..
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 = Exponential In the integra..Standard integrals
By method of completing squares ax 2 + bx + c is expressed as A 2 - X 2 or X 2 - A 2 or A 2 + x 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 or A 2 + x 2 and the integral reduces to which can be evaluated using the standard integrals..Integration by Parts
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 ..
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 ..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 ..Some Special Integrals
Prove that: ..
Prove that: ..
Integration of the form
Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..
Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..See what our Users say :
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