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Firstly, note that cos^2(x)+5sin^2(x)= cos^2(x) +sin^2(x) +4sin^2(x).
By trignoemtric identies, cos^2(x)+sin^2(x)=1 and so we can just integrate 1+4sin^2(x) since this is equal to cos^2(x...
Using the knowledge of a2 = b2 + c2 - 2bcCos(A)
Rearrange to aquire Cos(A) = (b2 + c2 - a2)/2bc
Then input ...
d/dx(4x3 + 2x) = d/dx (4x3) + d/dx(2x)
= 4(3x2) + x
= 12x2 + x
Suppose you are asked by your teacher to sum all the integers from 1 up to 1000. You might be thinking they must hold some kind of grudge against you. If you try to calculate the sum by adding on each ...
Notation: I use the ^ in the title question to indicated 'to the power of' and I use an asterisk * (or star) to indicate 'multiplied by' in the answer, to avoid confusion with the x term!
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