quotient rule of integration

(1) Let be rational function. If is improper, divide P(x) by Q(x). Let T(x) be the quotient and P 1 (x) be the remainder, then Where T(x) is a polynomial and is a proper rational function. (2) Resolve the proper rational function in to partial fractions. (3) Write as sum of partial fracti..

Quotient Rule for Differentiation - In this section, we derive the formulaIn this section, we derive the formula and use it to differentiate quotients of function..

Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Write and expr..

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..

Working rules for finding the greatest term: Step 1: In (a + b) n , the constants a and b must be positive. Step 2: Write T r+1 and T r and find the value of T r+1 /T r . Step 3: Simplify the inequality (T r+1 /T r ) greater than or equal to 1 and find the..

Approximate the definite integral ∫ 0 2 x ln ( x + 1) dx using Simpson's Rule with n = 4. => 1.123 or 1.8797 or 2.1972 or 4.9461 or 1.6487..

The measurements in an experiment to approximate an unknown continuous function y = f ( x ) are shown in table. Approximate the integral ∫ 0 1 f ( x ) dx using the Trapezoidal Rule. x 0 0.25 0.5 0.75 1 f ( x ) 1 1.5 2 2.5 3 => 3.5 or 3 or 4 or 2 or 2.5..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, intervals Newton's m..