# Some Important Integrals

Some Important Integrals (i) . (ii) . (iii) . Example: is equal to ? Solution: Given, , Here, we can convert the integrand into some standard integrand of the form and then integrate. Let,  , ,  (∵ ), , . Share +1 Tweet View Email Print Follow

# Integration by Parts

Integration by Parts If u and v are two functions of x, then i.e., the integral of the product of two functions = (first function) x (integral of second function) – integral of {diff of first function) x (integral of second function)} we can choose the first function which comes first in the word ILATE, where Read more about Integration by Parts[…]

# Fundamental Theorem of Calculus

Fundamental Theorem of Calculus The fundamental theorem of calculus is a theorem that likes the concept of the derivative of a function with the concept of the integral. (i) First fundamental theorem of calculus: Let f be a continuous real valued function defined on a closed interval [a, b]. let F be the function defined, Read more about Fundamental Theorem of Calculus[…]

# Integral Function and its Properties

Integral Function and its Properties Let f(x) be a continuous function defined on [a, b], then a function φ(x) defined by φ (x) = a∫x f (t) dt for all x ϵ [a, b] is called the integral function of the function f(x) Property I: The integral function of an integrable function is always continuous. Read more about Integral Function and its Properties[…]

# Differentiation – Implicit Function

Differentiation – Implicit Function i) In given implicit function, we solve this for dy/dx directly ii) Moderate level sometime in question, we asked dy/ dx at some particular point x. So, after getting dy/dx, we put the given particular value of x in dy/ dx and get the desired result. If the relation between the Read more about Differentiation – Implicit Function[…]

# Differentiation – Logarithmic

Differentiation – Logarithmic The function which can be evaluate by using logarithmic differentiation are of type y = [f (x)]g(x). y = f₁ (x). f₂ (x). f₃ (x) … . For this type of function take the logarithm and then differentiation. Example 1: If xy. yx = 1, then the value of =? Solution: Given that, Read more about Differentiation – Logarithmic[…]