What is f(x) = int xsinx dx if f(pi/3) = -2 ?

1 Answer
Nov 2, 2016

f(x) = -xcosx + sinx - 2.34, approximately.

Explanation:

Use integration by parts.

Let u = x and dv = sinxdx.

So, du = dx and v = -cosx

Now, use the integration by parts formula int(udv) = uv - int(vdu).

int(xsinx) = -xcosx - int(-cosx)

f(x) = -xcosx + sinx + C

Now, all we have to do is determine the value of C.

We know that when x = pi/3, y = -2, so:

-2 = -pi/3cos(pi/3) + sin(pi/3) + C

-2 + pi/3cos(pi/3) + sin(pi/3) = C

Evaluating using a calculator, you should get C ~=-2.34

Hopefully this helps!