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Question

1. Solve dy/dx = 4csc(x)cot(x) if y(2) = 1 

y(x) = -4csc(x) - 3.399 
y(x) = -4csc(x) + 5.399 
y(x) = -4csc(x) – 5.399 


2. Find the equation of the curve that passes through the point (0, 3) and has a slope at any point defined by y' = (-2)/(sqrt(1-x^2)) 

y(x) = 2sin-1(x) + 3 
y(x) = 2sin-1(x) – 3 – π 
y(x) = 2cos-1(x) – 3 + π 
y(x) = 2cos-1(x) + 3 – π 


3. If f(1) = 3, find the particular antiderivative of f′(x) = 2 csc^2 x. 

f(X) = -2 cot(x) + 1.003 
f(X) = -2 tan(x) + 1.003 
f(X) = -2 cot(x) + 4.284 
f(X) = -2 tan(x) + 4.284 


4. Find the anti-derivative of g(x) = 6 sin(x) that contains the point (π, 0). 

6 cos(x) – 6 
6 sin(x) – 6 
-6 cos(x) – 3 
-6 cos(x) – 6

 

 

Answer 1

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(4).