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numerator integral: 2, denominator integral: -2 (3 + x)√(4-x^2) dx
Solution
∫-2 2(3 + x)√(4-x^2) dx=
=3∫-2 2√(4-x^2) dx+∫-2 2x√(4-x^2) dx=
3∫-2 2√(4-x^2) dx is a table integral. But if you don’t the answer, you can evaluate by trigonometric substitution, say (You can substitute as x=cosu or x=sinu)
∫-2 2x√(4-x2) dx=-1/2∫-2 2√(4-x2) d(4-x2)= |Now you can substitute (4-x2) =u and evaluate]=
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