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Find the definite integral?

Find ∫ 1/(sqrt(4-x^2)) dx from 1 to 2.
 
Answer: (1/3)pi

Comments

Note that this is an improper integral since the integrand is undefined at 2. The integral is defined as
limb→2- ( ∫1b [4 - x2] dx )

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Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (140 lesson ratings) (140)
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the integral is sin-1(x/2) evaluated between 1 and 2 which is an angle whose sine is 1-an angle whose sine is 1/2 which is π/2-π/6=π/3
 
Regards
 
Jim
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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∫[4 - x2] dx = sin-1 (x/2) evaluated between 1 and 2
 
sin-1(2) - sin-1(1/2) = (1/3)pi
 

Comments

The way you get arcsin(x/2)from ∫dx/√(4-x2)=∫dx/(2√(1-(x/2)2)=∫d(x/2)/(√(1-(x/2)2)