- #1
ns5032
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How do I find the integral of:
1/[9.8 - (1/245)v^2]
1/[9.8 - (1/245)v^2]
The most efficient way to solve this integral is by using the substitution method. Let u = 9.8 - (1/245)v^2 and du = (-2/245)v dv. This will simplify the integral to ∫1/u du, which is a simple logarithmic function.
The number 9.8 represents the acceleration due to gravity on Earth in m/s^2. This integral is commonly used in physics problems involving gravitational force.
Yes, it is possible to solve this integral using partial fraction decomposition. However, this method may not be as quick as using substitution.
This integral can be applied to any value of v, as long as it is a real number. However, it is commonly used for values of v that represent velocities in physics problems.
Yes, this integral has practical applications in physics, specifically in calculating the work done by a varying gravitational force. It can also be used to calculate the potential energy of an object in motion.