1, Evaluate the definite integral. Use a graphing utility to confirm your result.

xsin 2xdx note integration of pi to 0 sin 2x dx

Step 1

To find the integralxsin 2xdx,

use the formula of integration by parts.

Letdv= sin 2xdx.

Integrate the differential equation to obtain the functionv.

v=dv=sin 2xdx=1

cos(x)

Letu=x. Differentiateuwith respect tox.

du=

2, Find the general solution of the differential equation. (UseCfor the constant of integration.)

dy

dx

=x²

x4

y=

3, Find the indefinite integral. (Note:Solve by the simplest methodnot all require integration by parts. UseCfor the constant of integration.) there are multiple steps

x radical x54 dx x-54 inside the radical

4, Solve the differential equation.

dr/dt 11e^t/radical 1-e^2t