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QUADRATURE, EXERCISE, Q.1, Area bounded by the curve xy – 3x - 2y - 10 = 0, x-axis and the lines x = 3, x = 4 is-, [1] 16 log 2– 13, [2] 16 log 2 - 3, [3] 16 log 2 + 3, [4] none of these, Q.2, Area bounded by the curve y = log x, x-axis and the ordinates x = 1, x = 2 is-, [1] log 4 sq. units, [2] log 4 + 1 sq. units, [3] log 4 – 1 sq. units, [4] none of these, Q.3, Area bounded by the curve y = sin x between x = 0 and x = 2n is-, [2] 4 sq. units, Area bounded by the parabola y = 2x and the ordinates x = 1, x = 4 is-, [1] 2 sq. units, [3] 8 sq. units, [4] none of these, Q.4, 4/2, 28/2, 56, [1], sq. units, [2], sq. units, [3], sq. units, [4] none of these, 3, 3, 3, Area bounded by the parabola y = 4x?, y-axis and the lines y = 1, y = 4 is-, [1] 3 sq. units, Area bounded by the lines y = x, x = -1, x = 2 and x-axis is-, Q.5, [2] 7/5 sq. units, [3] 14/3 sq. units, [4] none of these, Q.6, [1] 5/2 sq. units, Area between the curve y = cos x and x-axis when 0 <x is, [2] 3/2 sq. units, [3] 1/2 sq. units, [4] none of these, Q.7, [1] 2, Area bounded by curve y = x³, x-axis and ordinates x = 1 and x = 4 is-, [2] 4, [3] 0, [4] 3, Q.8, 127, 255, [1] 64 sq. units, [2] 27 sq. units, [3], sq. units, [4], sq. units, 4, 4, Q.9, Area bounded by curve y = k sin x between x = n and x = 2n is-, k?, [1] 2k sq. units, [2] 0, [3], sq. units, [4] k sq. units, Q.10, The area enclosed by the curve y = sin x, y = 0, x = 0 and x = t/2 is-, [2] 2n, [1] n, The area bounded by the curves y = 8x and y = x is, [3] 1, [4] 2, Q.11, 128, 32, 64, [1], 3, sq. units, [2], sq. units, [3], sq. units, [4] 32 sq. units, 3, 3, Q.12, The area of the loop between the curve y = asin x and x-axis is, [1] a, The area bounded by the curves y = x e , y = x e* and the line x = 1 , is, [2] 2a, [3] 3a, [4] none of these, Q.13, 2, 1, [3], 1, [1], [2] 1-, e, [4] 1-, e, Q.14, The area bounded by the curve y = x³ , the x-axis and the ordinates x = -2 and x = 1 is, [1] -9, The area enclosed within the curve |x| + ly = 1 is, [2] –15/4, [3] 15/4, [4] 17/4, Q.15, [1] 1, The area bounded by the curve x? = 4y and the straight line x = 4y-2 is, [1] 3/8, [2] 1.5, [3] 2, [4] None of these, Q.16, [2] 5/8, [3] 7/8, [4] 9/8, y?, =1 and the straight line, b2, y, = 1 is, b, Q.17, The area between, at, a, 1, 1, ab, 4, 1, nab, 4, 1, (11 jab, [3] z, [2], rab, [4], ab, 2, 106

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QUADRATURE, Q.18, The area bounded by the lines y = x , y = 0 and x = 2 is, [1] 1, [2] 2, [3] 4, [4] None, Q.19, The area bounded by the curve y = x sin x? , x-axis and x = 0 and x =, is, 2, [1] 1/2, [2] 1/ 2, [3] 1/4, [4] t/2, y, +1=0, x = -2, x = 3 and x-axis is, 4 2, Q.20, The area bounded between the curve, [1] 45/4, [2] 45/2, [3] 15, [4] 25/2, Q.21, The area bounded by curves y = tan x, x-axis and x =, is, [1] 2 log 2, [2] log 2, [3] log, V3, [4] 0, The area between the curve x? = 4 ay , x - axis, and ordinate x = d is, [1] d / 12a, Area bounded by the curve y = x (x-1)2 and x-axis is, [1] 4, The area bounded by the curve y = log x, x-axis and ordinate x-e is, [1] log,2, Q.22, [2] d/a, [3] d°/2a, [4] d/6a, Q.23, [2] 1/3, [3] 1/12, [4] 1/2, Q.24, 'e, [2] 1/2 unit, [3] 1 unit, [4] e unit, 1, The area bounded by the curve y =, Q.25, coordinates axes and x = T/4 is, cos? x, [2] 2, [4] 0, [1] 1, The area between the curve y = 4x , y-axis , and y = -1 and y = 3 is, [1] 7/3, The area bounded by the curve y = sin 2x , y-axis and the abscissa y = 1 is, [1] 1, The area between the curve x= 2y-y and y-axis is, [1] 9/4, The area bounded by the curve x = 8y, x-axis and the ordinate x = -2 , x = 4 is, [1] 4, The whole area of the curve 9x2 + 16y2 =144 is, [1] 24n, The area between the curve y = cos x and x-axis when a/2 < x < 2n will be -, [3] T/4, Q.26, [2] 9/4, [3] 1/12, [4] 1/4, Q.27, [2] 1/4, [3] T/4, [4] (t/4)(1/2), Q.28, [2] 4/3, [3] 9, [4] None of these, Q.29, [2] 2, [3] 1, [4] 3, Q.30, [2] 1447, [3] 6T, [4] 12n, Q.31, [4] 4, The area between the curve y = sin x, x-axis, and the ordinates x = 0 to x = t/2 is, [4] 3/2, [1] 1, [2] 2, [3] 3, Q.32, [1] 1, [2] 1/3, [3] 2/3, Q.33, The common area of the curves y = x and x =, Vy is, [1] 3, The area of a loop bounded by, [3] 1/3, curve y = a sin x and x-axis is, [3] 0, [2] 5/3, [4] None of these, Q.34, [2] 2a?, [1] a, The area bounded by y = 4x – x² and the x-axis is, [1] 30/7, The area contained between the x-axis and one arc of the curve y = cos 3x is, [1] 1/3, Area between the curves y = 4 + 3x – x² and x-axis is square unit is, [4] 2a, Q.35, [2] 31/7, [3] 32/3, [4] 34/3, Q.36, [2] 2/3, [3] 2/7, [4] 2/5, Q.37, [1] 125/3, [2] 125/4, [3] 125/6, [4] None of these, 107

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QUADRATURE, EXERCISE # 2, 8, 1+, X-axis and the ordinates x = 2, x = 4 into, x2, Q.1, If the ordinate x = a divides the area bounded by the curve y =, two equal parts, then a =, [1] 8, [2] 2/2, [3] 2, [4] /2, Q.2, Area under the curve y = 3x +4 between x = 0 and x = 4, is-, 56, 64, [2], sq. units, 9, [1], sq. units, [3] 8 sq. units, [4] none of these, Q.3, Area enclosed between the curve y?(2a – x) = x³ and line x = 2a above x-axis is-, Зл а?, [2], [3] 2n a?, [1] na?, [4] 3r a?, Q.4, The area bounded by the straight lines x = 0, x = 2 and the curves y = 2*, y = 2x – x² is-, 4, 1, [1] 3 log 2, 3, 4, 3, [2], log 2, 4, -1, [3], log 2, [4], log 2, 3, Q.5, The area bounded by curves y = cosx and y = sin x and ordinates x 0 and x =, is-, 4, [1] /2, [2] 2 +1, [3] 2-1, [4] 2(J2 -1), Q.6, If a curve y = avx + bx passes through the point (1, 2) and the area bounded by the curve, line x= 4 and x-axis, is 8 square units, then-, [1] a = 3, b = -1, [2] a = 3, b = 1, [3] a = -3, b = 1, [4] a = -3, b = -1, Q.7, The area of the figure bounded by the curves y = 2x + 1 and x - y- 1 = 0 is, [1] 2/3, [2] 4/3, [3] 8/3, [4] 16/3, Q.8, The area bounded by the curve y 2x - x2 and the straight line y = -x is given by, [1] 9/2, [2] 43/6, [3] 35/6, [4] None of these, Q.9, The area of the region bounded by y = |x -1| and y = 1 is, [1] 1, [2] 2, [3] 1/2, [4] None of these, Q.10, The area bounded by the curve y = x |x], x-axis and the ordinates x =1 , x = -1 is given by, [1] 0, 1, [2], [3], [4] None of these, 108

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QUADRATURE, Q.11, The area of the region lying between the line x - y + 2 = 0 and the curve x =, Vy is, 9., 10, [1] 9, [2], 2, [3], 3, [4] None of these, Q.12, If area bounded by the curves y = 4ax and y =mx is a?/3, then the value of m is, %3D, [1] 2, [2] -2, [3] 1/2, [4] None of these, Q.13, The area bounded by the curves y = x2 and y = |x| is, [1] 2/3, [2] 1/6, [3] 1, [4] 1/3, Q.14, Common area between the parabolas y = 2x2 and y = x2 +4 is, [1] 16/3, [2] 8/3, [3] 32/3, [4] None of these, Q.15, The area of the region bounded by the curve x + Vy = Va (x,y>0) and the coordinate axes is, [1] a?/6, [2] a?/2, [3] a?/3, [4] a?, Q.16, The area between the curves ay = 3 (a? - x2) and x-axis is-, [1] 4a?, [2] 6a?, [3] 9a?, [4] 12a?, 2, is, 1+ x2, Q.17, The area between the curves y = x2 and y =, 1, [1] T -, 2, [4] T +, [2] n – 2, [3] T-, 109