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Find the indefinite integral of sin(x)*e^x

As we are integrating, we must decide which method to use. As the integrand is of the form f(x)*g(x), integration by parts seems to make sense. Firstly, let L = INT(sin(x)*e^x). So we want to find L - this w...
CJ
Answered by Christopher J. • Maths tutor
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What the main differences between an interpreter and a compiler?

A compiler produces an object or executable file that can be manually run after the source code is compiled. On the other hand, the interpreter doesn't produce an executable file, rather it will simulate lin...
HS
Answered by Henry S. • Computing tutor
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Why does atmospheric pressure drop when altitude increases?

(Question can be sketched with a graph) Firstly, in order to have atmospheric pressure, air molecules must collide with a surface, in this case the face of the Earth. As you gain altitude (height from face o...
HS
Answered by Henry S. • Physics tutor
4148 Views

Given that: 2tanθsinθ = 4 - 3cosθ , show that: 0 = cos²θ - 4cosθ + 2 .

Starting with: 2tanθsinθ = 4 - 3cosθ . We can rewrite tanθ in terms of sinθ and cosθ.We know: tanθ = sinθ ÷ cosθ .By substituting we get: 2(sinθ ÷ cosθ)sinθ = 4 - 3cosθ .Let's multiply out by cosθ to get: 2s...
HS
Answered by Henry S. • Maths tutor
5733 Views

Write 9sin(x) + 12 cos(x) in the form Rsin(x+y) and hence solve 9sin(x) + 12 cos(x) = 3

9sin(x) + 12 cos(x) = Rsin(x+y) =R(sin(x)cos(y)+cos(x)sin(y))= (Rcos(y))sin(x) + (Rsin(y))cos(x)Therefore by matching the coefficientsRsin(y)=12, Rcos(y)=9 [1]SoRsin(y)/Rcos(y) = 12/9 = 4/3, therefore tan(y)...
JH
Answered by James H. • Maths tutor
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