Answer to Question #88003 in Math for Joshua

Question #88003
1.Find the integral with respect to x ∫cos x sin xdx
a.sin^2x
-------- +c
2
b.sin2x+c
c.cos^2x
----- +c
2
d.sinx
1
Expert's answer
2019-04-16T13:54:24-0400

Solution. Let y=sin(x), then dy=cos(x)dx. Make a substitution and get


"\\int sin(x)cos(x)dx = \\int ydy"

Using a table of integrals get


"\\int ydy= \\frac {y^2} {2} + C"

where C is constant. Returning to substitution get


"\\int sin(x)cos(x)dx =\\frac {sin^2(x)} {2}+ C"

where C is constant.

Answer. a.


"\\int sin(x)cos(x)dx = \\frac {sin^2(x)} {2}+ C"


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