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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

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

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

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

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

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

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

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 [...]