### Integration

> WEEKLY ACTIVITY

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#### Introduction to integration

 LEARNING OUTCOMES RESOURCES INTEGRATION REVISE INTEGRATION (35 LESSONS) INTEGRATION JOKE! POLYNOMILAS & EXPONENTIALS Anti-differentiation INTEGRATE POLYNOMIAL Negative/fractional powers NEGATIVE/FRACTIONAL POWERS Evaluating C EVALUATING THE CONSTANT Exponentials INTREGRATE EXP JOKE! 1/x INTEGRATING SIMPLE LOGARITHMIC TRIG FUNCTIONS Trig functions INTEGRATE TAN(2X) Trig products INTEGRATE TRIG PRODUCTS Chain rule UNDOING CHAIN RULE Quotients QUOTIENT RULE Rational INTEGRATE PROPER FRACTIONAL EXP    INTEGRATE IMPROPER FRACTIONAL EXP INTEGRATE POWERS OF SIN(X)   INTEGRATION SONG BY SUBSTITUTION Simple substitution SUBSTITUTION METHODCOMMON ERRORS Product substitution SUSTITUTION INETGRAL EXTENSION EXERCISE 16,17,18 SUBSTITUTE X=aTANx DEFINITE INT & AREAS & SOLIDS Evaluating integrals BASIC DEFINITE INTEG Applications AREA UNDER QUDRATIC FUNCTION WITH GRADIENT GIVEN  AREA UNDER CURVE Even/odd/periodic Area above & below AREA ABOVE AND BELOW AREA UNDER CURVE APP! Area between curves AREA BETWEEN CURVES Area with y-axis SLICE METHOD (FROM MINUTE 2:30) Rotation around x-axis VOLUME AROUND X-AXIS WASHER METHOD Rotation around y-axis VOLUME AROUND Y-AXISSHELL METHODVOLUME ABOUT ANY AXIS NUMERICAL INTEGRATION Speradsheet Trapezium rule TRAPEZIUM RULE Simpson´s rule SIMPSON´S RULE EXTENSION 19,20,21,22 PROBLEM OF THE WEEK DIFFERENTIAL EQ´S Writing eq´s Checking 1st order Checking 2nd order Solve simple dy/dx=f(x) Separate variables SEPARATE Y,X   SEPARATE V,T Particular solutions PARTICULAR SOLUTIONS Solve differential eq´s Newton´s cooling law NEWTON´S COOLING   NEWTON´S COOLING EXPERIMENT EXTENSION EXERCISE 23,24,25 NEWTONS COOLING PROBLEM