The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 is 1) (4√2 - 2)sq units 2) (4√2 + 2)sq units 3) (4√2 -1)sq units 4) (4√2 + 1)sq units Solution: (1) (4√2 - 2)sq units... View Article
The area (in sq units) bounded by the curve y = 1 + loge x, the X – axis and the straight line x = e is equal to 1) 3e - 2 2) e 3) e - 1/e 4) e + 1/e Solution: (2) e... View Article
Find the area of a curve xy = 4, bounded by the lines x = 1 and x = 3 and x-axis 1) log 12 2) log 64 3) log 81 4) log 27 Solution: (3) log 81... View Article
The area enclosed between y2 = x and y = x is 1) 2/3 sq units 2) 1/2 sq units 3) 1/3 sq units 4) 1/6 sq units Solution: (4) 1/6 sq units... View Article
If the area between y = mx2 and x = my2 (m > 0) is 1/4 sq units, then the value of m is 1) ± 3√2 2) ± 2/√3 3) √2 4) √3 Solution: (2) ± 2/√3... View Article
The area in the positive quadrant enclosed by the circle x2 + y2 = 4, the line x = y √3 and x-axis is 1) π/2 2) π/4 3) π/3 4) π Solution: (3) π/3 x2 + y2 = 4 --- (i) x = y √3 y = x / √3 ---- (ii)... View Article
The area of the region enclosed by the curves y = x, x = e, y = 1/x and the positive x-axis is 1) 1 sq units 2) 3/2 sq units 3) 5/2 sq units 4) 1/2 sq units Solution: (2) 3/2 sq units... View Article
If the straight line x = b divide the area enclosed by y = (1 – x)2, y = 0 and x = 0 into two parts R1 (0 ≤ x ≤ b) and R2 (b ≤ x ≤ 1) such that R1 – R2 = 1/4. Then, b equals 1) 3/4 2) 1/2 3) 1/3 4) 1/4 Solution: (2) ½... View Article
The area of the region bounded by the curves y = x3, y = 1/x, x = 2 is 1) 4 - loge 2 2) 1/4 + loge 2 3) 3 - loge 2 4) 15/3 - loge 2 Solution: (2) 1/4 + loge 2... View Article
The area bounded between the parabolas x2 = y/4 and x2 = 9y and the straight line y = 2 is 1) 20√2 2) 10√2 / 3 3) 20√2 / 3 4) 10√2 Solution: (3) 20√2 / 3... View Article
If S is the area of the region enclosed by y = e-x2, y = 0, x = 0 and x = 1. Then, 1) S ≥ 1 / e 2) S ≥ 1 - (1 / e) 3) S ≤ (1 / 4) [1 + (1 / √e)] 4) S ≤ (1 / √2) + (1 / √e) [1 - (1 / √2)] Solution: (2) S ≥ 1 - (1 / e)... View Article
The area bounded by the curves y = ex, y = e-x, straight line x = 1 is given by 1) e + e-1 - 2 2) e - e-1 3) e + e-1 4) e + e-1 + 2 Solution: (1) e + e-1 - 2... View Article
The area bounded by the curves y = x and y = x3 is equal to 1) 0 2) 1/4 3) 1/2 4) 1 Solution: (3) ½ The line y = x lies above the curve y = x3 in the first quadrant and y = x3 lies above the line... View Article
Area included between the parabola y = x2 / 4a and the curve y = 8a3 / (x2 + 4a2) is 1) (a2 / 3) (6Ï€ - 4) 2) (a2 / 3) (4Ï€ + 4) 3) (a2 / 3) (8Ï€ + 3) 4) None of these Solution: (1) (a2 / 3) (6Ï€ - 4) The curve of... View Article
The area (in sq units) of the region bounded by the curves y2 = 4ax and x2 = 4ay, a > 0 is 1) 16 (a2 / 3) 2) 14 (a2 / 3) 3) 13 (a2 / 3) 4) 16a2 5) None of these Solution: (1) 16 (a2 / 3)... View Article
The area (in sq units) bounded by the curves y = √x, 2y – x + 3 = 0, x-axis and lying in the first quadrant is 1) 9 2) 6 3) 18 4) 27/4 Solution: (1) 9... View Article
The area enclosed by the curves y = sinx + cos x and y = |cos x – sin x| over the interval [0, Ï€/2] is 1) 4(√2 - 1) 2) 2√2(√2 - 1) 3) 2(√2 + 1) 4) 2√2(√2 + 1) Solution: (2) 2√2(√2 - 1)... View Article
The area enclosed between the curves y = x3 and y = √x is 1) 5/3 2) 5/4 3) 5/12 4) 12/5 Solution: (3) 5/12... View Article
The area (in sq units) of the region bounded by x = – 1, x = 2, y = x2 + 1 and y = 2x – 2 is 1) 10 2) 7 3) 8 4) 9 Solution: (4) 9... View Article
Area bounded by the curve x = 0 and x + 2|y| = 1 is 1) 1/4 2) 1/2 3) 1 4) 2 Solution: (2) ½... View Article
