How to prove the volume of a cone(opens in new window) How to find the area between two curves Elliptic Integrals An elliptic integral is an integral with the form Here R is a rational function of its two arguments, w, and x, and these two arguments are related to each other by thes...
I = 0∫π/2log[(sinx. cos x)/sin2x]dx We know that sin2x= 2 sinx cos x) Now, the integral expression can be written as I = 0∫π/2log[(sinx. cos x)/(2 sinx cos x)]dx Cancel the terms which are common in both numerator and denominator, then we get I = 0∫π/2 log...
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Solution: By adding and subtracting in the numerator we can simplify this rational function as follows: Note that if we integrate this result, we obtain s + 5 ln |s − 3| + C. Compare this with the result of Example 3: can you explain why both answers are correct? 4 Partial Fracti...
, the gamma factors appearing in the numerators of the line integrals must be expanded in bracket series. this guarantees that the method provides all series representations of the solution. as usual series converging in a common region must be added. it is the heuristic observation that the ...
The second heuristic simply replaces all expressions equal to g(x) by u, then hope that all remaining occurrences of x is in a single g (x) in the numerator. Note that the user can always first rewrite the expression into a form where the second heuristic can be applied. 4.2 Rational...