Home/Tag: Integration
30 07, 2018

Integral Calculus

By |2018-07-30T09:44:35+10:00July 30th, 2018|Tags: , , , |Comments Off on Integral Calculus

Financial Maths Go to the Financial Maths Forum to see more questions or ask your own Topics Covered in Financial Maths Continuous Probability Distributions Normal Distribution Standard Normal Distribution Formulas used in Financial Maths  $$y=mx+b$$ $$m=\frac{rise}{run}$$ b = y-intercept [...]

30 07, 2018

Anti-Derivative

By |2018-07-30T09:40:17+10:00July 30th, 2018|Tags: , , |Comments Off on Anti-Derivative

Financial Maths Go to the Financial Maths Forum to see more questions or ask your own Topics Covered in Financial Maths Continuous Probability Distributions Normal Distribution Standard Normal Distribution Formulas used in Financial Maths  $$y=mx+b$$ $$m=\frac{rise}{run}$$ b = y-intercept [...]

7 02, 2017

t Method

By |2017-02-07T15:32:05+10:00February 7th, 2017|Tags: , , |0 Comments

t Method   worked examples Find $$\int{\ln x\,dx}$$. $$=\int{1.\ln x\,dx}$$ rewrite as $$\int{\ln x\,dx} $$ let f(x) = ln x    g'(x) = 1 select f(x) = ln x and g'(x) = 1 when selecting which part to make f(x) and which part to make g'(x), we want [...]

24 01, 2017

Integrating Trig

By |2017-02-07T17:15:00+10:00January 24th, 2017|Tags: , , |0 Comments

Integrating Trig Useful Identities $$\tan^2\theta=1-\sec^2\theta$$ $$=1-\frac{1}{\cos^2\theta}$$ $$=\frac{cos^2\theta-1}{cos^2\theta}$$ $$=1-\frac{1}{cos^2\theta}$$ worked examples Find $$\int{\frac{1}{\cos x}\,dx}$$. $$\int{\frac{\cos x}{\cos^2 x}\,dx}$$ rewrite as $$\int{\frac{\cos x}{\cos^2 x}\,dx}$$ $$\int{\frac{\cos x}{1-\sin^2 x}\,dx}$$ we know cos2 x = 1 - sin2 x let u = sin x du = cos x dx let u = sin [...]

2 01, 2017

Integration By Parts

By |2017-02-07T17:01:45+10:00January 2nd, 2017|Tags: , , |0 Comments

Integration By Parts $$\int f(x).g'(x)\,dx=f(x).g(x)-\int f'(x).g(x)\, dx$$ worked examples Find $$\int{\ln x\,dx}$$. $$=\int{1.\ln x\,dx}$$ rewrite as $$\int{\ln x\,dx} $$ let f(x) = ln x    g'(x) = 1 select f(x) = ln x and g'(x) = 1 when selecting which part to make f(x) and which part to make g'(x), [...]

2 01, 2017

Dividing Complex Numbers

By |2017-01-11T18:48:38+10:00January 2nd, 2017|Tags: , , , |0 Comments

Dividing Complex Numbers $$\overline{a+ib}=a-ib$$ worked examples Simplify (7 + 2i) ÷(3 + 3i). $$=\frac{{7 + 2i}}{{3 + 3i}}$$ rewrite in fraction form to make it simpler to see and work with $$=\frac{{7 + 2i}}{{3 + 3i}} \times \frac{{3 - 3i}}{{3 - 3i}}$$ multiply by the conjugate of the denominator [...]

26 12, 2016

Integration

By |2018-12-10T10:44:49+10:00December 26th, 2016|Tags: , |0 Comments

Integration Go to the Integration forum to see more questions or ask your own Topics Covered in Integration Standard Integrals Splitting The Numerator Partial Fractions Trig Functions t Formulae Integration By Parts Recurrence Definite Integrals   [...]

26 12, 2016

Standard Integrals

By |2017-01-02T08:19:23+10:00December 26th, 2016|Tags: , , |0 Comments

Standard Integrals $$\int {{x^n}\,dx = \frac{{{x^{n + 1}}}}{{n + 1}} + c}$$ $$\int {\frac{1}{x}\,dx = \ln \,x\, + c} $$ $$\int {{e^{ax}}\,dx = \frac{{{e^{ax}}}}{a} + c} $$ $$\int {\sin \,ax\,dx\, = \,\frac{{ - \cos \,ax}}{a} + c}$$ $$\int {\cos \,ax\,dx\, = \,\frac{{\sin \,ax}}{a}c} $$ $$\int {{{\sec }^2}\,ax\,dx = \frac{{\tan [...]

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