Use a trigonometric identity to evaluate ∫ (sin^2 x)/(cos^2 x) dx. Then use this to find the volume of the solid that is obtained by rotating the region bounded by the curves y = sec x, y = 1, and the lines x = 0, x = 1 about the x-axis.
Could someone help me out with this confusing question. The working out would also help me a lot.
Thanks.
Finding volume of a solid...?
2013-05-21 10:37 am
回答 (3)
2013-05-21 11:35 am
✔ 最佳答案
∫ sin^2x/cos^2x dx= ∫ tan^2x dx
= ∫ sec^2x - 1 dx (the identity of sin^2x + cos^2x = 1 divided by cos^2x)
= tanx - x + C
Solve by the disk method: ∫ π [f(x)]^2 dx.
∫ [0, 1] π [sec^2x - 1^2] dx, where ∫ [0, 1] π 1^2 dx is the hole of the solid
= [tanx - x] [0, 1]
= tan1 - 1 - tan0 + 0
= tan1 - 1 or 0.5574 (if the x of the tanx is in radian)
2016-11-05 6:15 pm
Take the 72ab8af56bddab33b269c5964b2662antegral from 0 to 2 of (x+2) - (x^2), w72ab8af56bddab33b269c5964b2662ath res72ab8af56bddab33b269c5964b2662aect to x to get the section between the two funct72ab8af56bddab33b269c5964b2662aons. Then take the 72ab8af56bddab33b269c5964b2662antegral from 0 to 2[72ab8af56bddab33b269c5964b2662a72ab8af56bddab33b269c5964b2662a] of the end result mult72ab8af56bddab33b269c5964b2662a72ab8af56bddab33b269c5964b2662al72ab8af56bddab33b269c5964b2662aed by utilising
2013-05-21 11:44 am
Why is this not in the math section?
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