Bài tập Toán INTEGRATION 17

Created by T Madas Question 48 (****) y N M y = x − x4 O x The diagram below shows the quartic curve with equation y = x − x4 , x ∈ » The point M is the maximum point on the curve and the point N lies on the y axis so that the straight line segment MN is parallel to the x axis Find the exact area of the shaded region, bounded by the curve, the y axis and the straight line segment from M to N area = 40 Created by T Madas Created by T Madas Question 49 (****) y y = x2 − x + A O D B C x The figure above shows a quadratic curve with equation y = x2 − x + The points A , B and C are the points where the curve meets the coordinate axes The point D lies on the curve so that AD is parallel to the x axis Calculate the exact area of the shaded region, bounded by the curve, the x axis and the straight line segment BD area = 19 Created by T Madas Created by T Madas Question 50 (****) y L R O y = x2 − x + 2 P Q x The diagram above shows the quadratic curve C with equation y = x2 − x + 2 The curve crosses the x axis at the points P and Q , and the y axis at the point R The line L is the tangent to C at the point P a) Find an equation of L b) Find the exact area of the shaded region bounded by the tangent at P , the curve and the y axis y + x = 10 , area = Created by T Madas