The bell-shaped curve x=e−y2 encloses, with the y–axis, a region T for −2≤y≤2.
(a) Write a definite integral that gives the exact area of T.
(b) Explain clearly why the antiderivative of the integrand in part (a) cannot be expressed in terms of elementary functions.
(c) Use the Trapezoidal Rule with four subintervals of equal length to approximate the area of T. Show all numerical work to at least three decimal places.
(d) Justify whether the approximation obtained in part (c) is an overestimate or an underestimate of the exact area, citing an appropriate property of the integrand.