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/Tag: Integration
30 07, 2018

## Integral Calculus

By |2018-07-30T09:44:35+10:00July 30th, 2018||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||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 [...]

29 06, 2017

## Volume Between Two Curves

By |2017-06-29T18:29:10+10:00June 29th, 2017||0 Comments

Volume Between Two Curves worked examples The area enclosed between the curves y = x2 and y = x3 is rotated about the x-axis. Find the volume of the solid formed. x3 = x2 x3 - x2 = 0 x2(x - 1) = 0 x = 0, x [...]

7 02, 2017

## t Method

By |2017-02-07T15:32:05+10:00February 7th, 2017||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 [...]

7 02, 2017

## Integration Recurrence

By |2017-02-07T15:25:50+10:00February 7th, 2017||0 Comments

Integration Recurrence 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 the [...]

24 01, 2017

## Integrating Trig

By |2017-02-07T17:15:00+10:00January 24th, 2017||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||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||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||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 [...]