Application of Integrals
Let f: be a continuous function such that f(x) = f( 1 −x) for all x . Let , and R2 be the area of the region bounded by y = f(x), x = -1, x = 2, and the x − axis. Then
Let the straight line x = b divide the area enclosed by y = , y = 0 and x = 0 into two parts and R2 such that . Then b equals
The area of the region bounded by the curves y = f(x), the x − axis, and the lines x = a and x = b, where , is
If , f(x) is a quadratic function and its maximum value occurs at point V. A is the point of intersection of y = f(x) with the x-axis and point B is such that chord AB subtends a right angle at V. What is the area enclosed by f(x) and chord AB?