Partial fractions - integration techniques, Mathematics

Assignment Help:

Partial Fractions - Integration techniques

In this part we are going to take a look at integrals of rational expressions of polynomials and again let's start this section out with an integral which we can already do so we can contrast it with the integrals that we'll be doing in this segment.

 ∫ (2x-1 / x2 -x - 6) (dx)

∫ (1/u) (du)

By using u = x2 - x - 6 and du = (2x-1) dx

= 1n |x2 - x - 6 | + c

Thus, if the numerator is the derivative of the denominator (or a constant multiple of the derivative of the denominator) doing this type of integral is fairly simple.  Though, frequently the numerator isn't the derivative of the denominator (or a constant multiple).  For instance, consider the following integral.

∫ (3x+11/(x2-x-6)) (dx)

In this type of case the numerator is certainly not the derivative of the denominator nor is it a constant multiple of the derivative of the denominator. Hence, the simple substitution which we used above won't work.  Though, if we notice that the integrand can be broken up as follows,

1546_Partial Fractions - Integration techniques 1.png

3x + 11 /x2-x-6

= 4/x-3 - 1/x+2

Then the integral is in fact quite simple.

556_Partial Fractions - Integration techniques 2.png


Related Discussions:- Partial fractions - integration techniques

Compound interest, you have RM5O,OOO to invest,and two fund that you''d li...

you have RM5O,OOO to invest,and two fund that you''d like to invest in.The You-Risk-It Fund yields 14% interest.The Extra-Dull Fund yields 6% interest.Besause of college financial-

Math, #question.help.

#question.help.

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

Logarithms, We know that 2 4 = 16 and also that 2 is referred to as ...

We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2

Point-slope form, The next special form of the line which we have to look a...

The next special form of the line which we have to look at is the point-slope form of the line. This form is extremely useful for writing the equation of any line.  If we know that

Calculate the height of the tunnel and the perimeter, The adjoining figure...

The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m (i.e., OA=3.5m) and ∠AOB=90 o . Calculate : i.       the height of the

Operation on polynomial, Perform the denoted operation for each of the foll...

Perform the denoted operation for each of the following.  (a) Add 6x 5 -10x 2 + x - 45 to 13x 2 - 9 x + 4 .   (b) Subtract 5x 3 - 9 x 2 + x - 3 from       x 2+ x +1.

Measures of dispersion- measures of central tendency, Measures of Dispersio...

Measures of Dispersion - The measures of dispersion are extremely useful in statistical work since they indicate whether the rest of the data are scattered away from the mean

Polynomials, simplify the expression 3/5/64

simplify the expression 3/5/64

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd