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:
7
Step-by-step explanation:
heres a model
A ----------R---------D
A ----?-----R----8---D
A----------15----------D
15 - 8 = 7
AR = 7
Answer:
the area of the cover will be
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes. oval/ellipse
the area of the ellipse is 
.
Since we are multiplying two units of length together, our answer will be in units squared.
also the oval/ ellipse has to radius major and minor radius
Given data
minor radius = a= 10 feet
major radius= b= 26 feet
furthermore we want the cover to extend 1 feet
hence
minor radius = a= 11 feet
major radius= b= 27 feet
