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∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + cDetailed derivation of∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx
= ∫(cosec2x - cosecxcotx)/(cosecx - cotx) dx
= log[cosecx - cotx] = log[(1-cosx)/sinx]
= log[2sin2(x/2)/2sin(x/2)cos(x/2)]
= log[tan(x/2)]
Determine the function f ( x ) . f ′ ( x )= 4x 3 - 9 + 2 sin x + 7e x , f (0) = 15 Solution The first step is to integrate to fine out the most general pos
Jon ran around a track that was one eighth of a mile long.He ran around the track twenty four times.How many miles did Jon run in all
Prove that if x is a real number then [2x] = [x] + [x + ½ ] Ans: Let us consider x be any real number. It comprises two parts: integer and fraction. With no loss of
Review: Systems of Equations - The traditional initial point for a linear algebra class. We will utilize linear algebra techniques to solve a system of equations. Review: Matr
1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step
alternate segment theorum
how do you divide decimals
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
It's now time to do solving systems of differential equations. We've noticed that solutions to the system, x?' = A x? It will be the form of, x? = ?h e l t Here l and
Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol
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