SOLUTION: Please help me solve this equation:
Evaluate the following integrals using trigonometric substitutions.
a) {{{ int ( x^2 / ( sqrt (1-(x^2) ) ), dx ) }}}
b) {{{ int ( 1/ (sqrt (
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Question 355862: Please help me solve this equation:
Evaluate the following integrals using trigonometric substitutions.
a)
b)
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use a substitution.
Let ,
.
.
.
Take it from there and solve for the integral in u, then back substitute to x.
.
.
.
Complete the square in the denominator.
Substitute, let ,
Substitute again, let ,
Take it from here and get the solution in v, back substitute for u, and then back substitute for x.
.
.
.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a) Hint: Draw a triangle with legs of , and with a hypotenuse of . So ('x' is the leg opposite the angle ). So because , d\theta)
So the integral then transforms to
}{\sqrt{1-\sin^2(\theta)}}\cos(\theta)d\theta)
But we know that }=\cos(\theta))
, so...
}{\cos(\theta)}\cos(\theta)d\theta)
and then the cosine terms cancel to leave you with
d\theta)
Let me know if this is enough to get you started.
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