Question

To find the surface area obtained by rotating the curve y=cos(x) from x=0 to x= π/2

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about the x axis, we first find dy/dx​ =

Answer 1

To find dy/dx for the equation y=cos(x), differentiate it with respect to x.

Step-by-step explanation:

To find the surface area obtained by rotating the curve y=cos(x) from x=0 to x=π/2 about the x-axis, we first find dy/dx.

To find dy/dx, we differentiate the given equation y=cos(x) with respect to x. The derivative of cos(x) is -sin(x). Therefore, dy/dx = -sin(x).

Answer 2

To find the surface area obtained by rotating the curve y=cos(x) from x=0 to x= π/2​ about the x axis, we first find dy/dx = -sin(x).

Step-by-step explanation:

Formula for Surface Area: The surface area (S) of a solid of revolution generated by rotating a curve y=f(x) around the x-axis between x=a and x=b is calculated using the formula:

S = ∫[a,b] 2πy √(1 + (dy/dx)^2) dx

Differentiate y=cos(x): To apply the formula, we need to find the derivative of y=cos(x), which is dy/dx = -sin(x).

Substitute and Integrate: Plugging y=cos(x), dy/dx=-sin(x), a=0, and b=π/2 into the formula, we get the integral expression for the surface area:

S = ∫[0, π/2] 2πcos(x) √(1 + (-sin(x))^2) dx

Solving the integral: This integral can be solved using various methods like trigonometric substitution or numerical integration to obtain the final surface area value.

Therefore, finding dy/dx = -sin(x) is the first step in calculating the surface area using the formula for solids of revolution.