Consider the region R bounded by y = 1 / (x^2 + 3x + 2) , x = 0, x = 1 and the x-axis.
Express your answer exactly with at most one logarithm in the answer.
Find the volume of the solid formed by rotating R about the x-axis.
I need help with this problem.
I believe I am supposed to take the integral from 0 to 1 of pi(1 / (x^2 + 3x + 2))dx
I use partial fraction decomposition and get ...
1 = A(x+3)(x-1)^2 + B(x-1)^2 + C(x+3)^2(x-1) + D(x+3)^2
From substituting x = 1, D = 1/16
and x = -3, B = 1/16
I need help finding A and C. and I am also wondering if my reasoning is correct so far.