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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,
3x + 11 /x2-x-6
= 4/x-3 - 1/x+2
Then the integral is in fact quite simple.
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-
#question.help.
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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
v=u+at s=ut+1/2at^2
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
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
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 - 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
simplify the expression 3/5/64
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