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How do you integrate sin^2(3x)cos^3(3x) dx?

Use the identity sin^2(y) + cos^2(y) = 1 to get the expression sin^2(3x) (1-sin^2(3x)) cos(3x) dx.Use the substitution u= sin(3x) by dividing the expression by the derivative, u’= 3cos(3x).The expression the...
ZG
Answered by Zachary G. • Maths tutor
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two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u

ball A has mass m and velocity u. ball B has mass 2 m and velocity 2uby conservation of momentum:mu - 4mu = mv + 2mx (1)where v is the velocity of ball A and x is the velocity of ball B after collision.by co...
WA
Answered by William A. • Maths tutor
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Find, using calculus, the x coordinate of the turning point of the curve with equation y=e^3x cos 4

1st step: find the derivative dy/dx of the given equation2nd step: now equate the obtained derivative to 0 because this is precisely the situation in which the graph changes direction (the derivative dy/dx e...
UW
Answered by Urszula W. • Maths tutor
4670 Views

How can I recognise when to use a particular method for finding an integral?

Often the question will ask you to use a particular method to integrate something, but sometimes they will not and you will have to recognise for yourself the best way to do it. There is often more than one ...
LC
Answered by Lloyd C. • Maths tutor
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If f(x)=x^2 and g(x)=5x-11, then what is fgg(x) when x=3?

g(3)=5(3)-11=15-11= 4 gg(3)=g( 4 )=5(4)-11= 20-11= 9 fgg(3)=f( 9 )=9 2 =81 fgg(3)=81
SM
Answered by Simon M. • Maths tutor
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