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December 3rd, 2007, 11:47 AM   #1
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From: phoenix

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Integral Problem

So ive been trying to tackle this problem for a while now and im sure there is something very simple that im missing.

Part A. Evaluate the integral by multiplying the numerator by an appropriate expression.

a. S(1/1+sin(x))dx

than part b is use the double angle formula to evaluate the integral-

b. S(1/1+cos2x)dx

Thanks alot ahead of time.

p.s. if there is any confusion on the S its suppose to be the stretched out s not a variable.
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December 3rd, 2007, 01:51 PM   #2
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You need parentheses to calarify the expressions to be integrated. If the trig function is supposed to be part of the denominator, put () around the whole denominator.
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December 3rd, 2007, 07:57 PM   #3
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a. S((1)/(1+sin(x)))dx

b. S((1)/(1+cos2x))dx
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December 4th, 2007, 10:18 AM   #4
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a. Multiply the numerator and denominator by (1-sin(x)). The denominator becomes 1 - sin(x)^2, which is cos(x)^2. Then you can expand the fraction to become 1/cos(x)^2 - sin(x)/cos(x)^2. Now this is easy to integrate.

b. Substitute the double angle formula for cos(2x), being 2cos(x)^2 - 1. You're left with 1/(2cos(x)^2), which should be easy.
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