Presentation on theme: "Review Problem – Riemann Sums Use a right Riemann Sum with 3 subintervals to approximate the definite integral:"— Presentation transcript:
Review Problem – Riemann Sums Use a right Riemann Sum with 3 subintervals to approximate the definite integral:
Applications of the Definite Integral Mr. Reed AP Calculus AB
Finding Areas Bounded by Curves To get the physical area bounded by 2 curves: 1.Graph curves & find intersection points – limits of integration 2.Identify “top” curve & “bottom” curve OR “right-most” curve & “left-most” curve 3.Draw a representative rectangle 4.Set up integrand: Top – Bottom Right – Left
Finding Intersection Points Set equations equal to each other and solve algebraically Graph both equations and numerically find intersection points
Example #1 Find the area of the region between y = sec 2 x and y = sinx from x = 0 to x = pi/4.
Example #2 Find the area that is bounded between the horizontal line y = 1 and the curve y = cos 2 x between x = 0 and x = pi.