MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
A curve is defined by y=1+x21 for x≥0. A region R is formed by the graph of the curve, the x–axis, and the y–axis, and it extends infinitely far to the right.
Answer the following questions about the region R.
(a) Sketch the region R on a set of coordinate axes and clearly label all intercepts and asymptotic behavior.
(b) Express the area of R as a single definite integral that involves a limit. Clearly indicate all limits of integration.
(c) Without evaluating the integral you wrote in part (b), use limit reasoning to explain whether the area of R is finite or infinite.