Integrals involving quadratics - integration techniques, Mathematics

Assignment Help:

Integrals Involving Quadratics

To this point we have seen quite some integrals which involve quadratics.  Example of Integrals Involving Quadratics is as follow:

∫ (x / x2 + a) (dx) = ½ 1n |x2 + a| + c

∫ (1/ x2 + a2) (dx) = 1/a tan-1 (x/a)

We as well saw that integrals including  √ (b2 x2 - a2), √ (a2 - b2 x2) and √ (a2 + b2 x2) could be done with a trig substitution.

Notice though that all of these integrals were missing an x term.  They all contain a quadratic term and a constant.

A few integrals including general quadratics are easy enough to do.  For example, the following integral can be done along with a quick substitution.

606_Integrals Involving Quadratics - Integration Techniques.png

Some integrals along with quadratics can be completed with partial fractions.  For example,

∫ (10x - 6 /( 3x2 + 16x+5)) dx

= ∫ ((4/x+5) - (2/3x+1)) dx = 4 1n |x+5| - 2/3 1n |3x+1| + c

Unfortunately, these techniques won't work on a lot of integrals.  A simple substitution will just only work if the numerator is a constant multiple of the derivative of the denominator and partial fractions will only work if the denominator can be factored.


Related Discussions:- Integrals involving quadratics - integration techniques

Combination, Combination A combination is a group of times whether ord...

Combination A combination is a group of times whether order is not significant. For a combination to hold at any described time it must comprise of the same items however i

Problem solving, compare 643,251;633,512; and 633,893. The answer is 633,51...

compare 643,251;633,512; and 633,893. The answer is 633,512

Systems of linear equation, a man can row a bangka at a rate of 5 km/h in s...

a man can row a bangka at a rate of 5 km/h in still water. It takes 10 minutes longer to row upstream a distance of 2km than he takes to row downstream. What is the rate of the cur

probability problems, A school principal is looking at the combinations of...

A school principal is looking at the combinations of subjects students are studying. He learns that the probability that a student is studying Chemistry is 0.5 and that the prob

Mensuration, find the diameter of circle whose circumference is 26.51

find the diameter of circle whose circumference is 26.51

Rectilinear figure, In a parallelogram ABCD AB=20cm and AD=12cm.The bisecto...

In a parallelogram ABCD AB=20cm and AD=12cm.The bisector of angle A meets DC at E and BC produced at F.Find the length of CF.

Kara brought $23 with her when she went shopping, Kara brought $23 with her...

Kara brought $23 with her when she went shopping. She spent $3.27 for lunch and $14.98 on a shirt. How much money does she have left? The two items that Kara bought must be sub

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