# What is the surface area of the solid created by revolving #f(x) = e^(x)/2 , x in [2,7]# around the x axis?

The area is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the surface area of the solid created by revolving ( f(x) = \frac{e^x}{2} ), ( x ) in ([2,7]) around the x-axis, you can use the formula for the surface area of a solid of revolution:

[ S = 2\pi \int_{a}^{b} f(x) \sqrt{1 + \left( f'(x) \right)^2} , dx ]

Where ( a = 2 ) and ( b = 7 ). First, find ( f'(x) ) which is ( \frac{1}{2}e^x ). Then plug these values into the formula:

[ S = 2\pi \int_{2}^{7} \frac{e^x}{2} \sqrt{1 + \left( \frac{1}{2}e^x \right)^2} , dx ]

After solving the integral, the surface area ( S ) will be the result.

By signing up, you agree to our Terms of Service and Privacy Policy

- Given #x^t * y^m - (x+y)^(m+t)=0# determine #dy/dx# ?
- What is the surface area of the solid created by revolving #f(x) = e^(x-2) , x in [2,7]# around the x axis?
- If #x^2 y=a cos#x, where #a# is a constant, show that #x^2 (d^2 y)/(dx^2 )+4x dy/d +(x^2+2)y=0 #?
- What is the arclength of #f(x)=e^(1/x)/x-e^(1/x^2)/x^2+e^(1/x^3)/x^3# on #x in [1,2]#?
- What is the general solution of the differential equation #(1+x^2)dy/dx + xy = x #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7