Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
Answer:
answer below
Step-by-step explanation:
I think you mean "squashed" or "stretched" vertically by a factor of 5.
f(x) is the original parabola equation
g(x) = 5f(x) is vertically stretched by a factor of 5
(x,y) -> (x , 5y)
The answer would be c I know cause I got it right on the test!
Answer:
41/3 - 14 - Square root of 200
Step-by-step explanation:
41/3 is between 13 and 14
14 is 14
Square root of 200 is between 14 and 15
