Practice Test


1) The area bounded by the curve y = x|x|, X- axis and the coordinates x = -1 and x = 1 is given by


2) Using integration, the area of the region bounded by the line
2y = 5 x + 7, X - axis and the lines x = 2 and x = 8 is


3) The area bounded by the curve
|x| + y = 1 and axis of x is


4) The area of the region bounded by the curve xy -3x -2y -10 = 0, X-axis and the lines x = 3, x = 4, is


5) The area bounded by x = 1, x = 2, xy = 1 and X-axis is


6) Using integration the area of region bounded by the triangle whose vertices are (-1,0), (1,3) and (3,2) is


7) The larger of the area bounded by y = cos x, y = x + 1 and y = 0 is


8) A curve y = f(x) passes through the origin and lies entirely in the first quadrant. Through any point P(x, y) on the curve, lines are drawn parallel to the coordinate axes. If the curve divides the area formed by these lines and coordinates area in m : n, then the value of f(x) is equal to


9) The area bounded by the curve
y = log x, y = log |x|, y = | log x | and y = | log |x|| is


10) The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one such region is


11) Let y be the function which passes through (1, 2) having slope
(2x + 1). The area bounded between the curve and X- axis is


12) Area bounded by the curve
y = (x - 1) (x - 2) (x - 3) and x-axis lying between the ordinates x = 0 and x = 3 is equal to


13) The area bounded by the graph y = |[ x-3]|, the X-axis and the lines x = -2 and x = 3 is ( [.] denotes the greatest integer function )


14) The slope of the tangent to a curve y = f(x) at { x, f(x) } is 2x + 1. If the curve passes through the point (1, 2), then the area of the region bounded by the curve, the X-axis and the line x = 1 is


15) Area bounded by lines y = 2 + x, y = 2 - x and x = 2 is


16) The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one of such region is


17) Ratio of the area cut off a parabola by any double ordinate is that corresponding rectangle contained by
that double ordinate and its distance from the vertex is