Answer to Question #88003 in Math for Joshua

Question

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

Answer 1

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.

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