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
Area (in sq units ) bounded by the curves y = ex, y = e-x and the straight line x = 1 is 1) e + (1 / e) 2) e + (1 / e) + 2 3) e + (1 / e) - 2 4) e - (1 / e) + 2 5) e - (1 / e) Solution: (3) e + (1 / e) - 2... View Article
The area of the region bounded by two parabolas y = x2 and x = y2 is 1) 1/4 2) 1/3 3) 4 4) 3 Solution: (2) â…“ The given two curves are parabola y = x2 and y2 = x. The point of intersection of these two... View Article
The area of the region bounded by the lines y = mx, x = 1, x = 2 and x-axis is 6 sq units, then m is equal to 1) 3 2) 1 3) 2 4) 4 Solution: (4) 4 Area enclosed = ∫12 mx dx = m [x2 / 2]12 = (m / 2) [3] (3m / 2) = 6 m = 4... View Article
The area of the region bounded by 1 – y2 = |x| and |x| + |y| = 1 is 1) 1/3 sq units 2) 2/3 sq units 3) 4/3 sq units 4) 1 sq units Solution: (2) 2/3 sq units... View Article
The area enclosed by the curves |y + x| ≤ 1, |y – x|≤ 1 and 2x2 + 2y2 = 1 is 1) [2 + (π / 2)] sq units 2) [2 - (π / 2)] sq units 3) [3 + (π / 2)] sq units 4) [3 - (π / 4)] sq units Solution: (2) [2 - (Ï€ / 2)]... View Article
The area bounded by y = x|sin x| and x-axis between x = 0, x = 2π is 1) 2 π sq units 2) 3 π sq units 3) π sq units 4) 4π sq units Solution: (4) 4π sq units... View Article
The area bounded y = xe|x| and line |x| = 1, y = 0 is 1) 4 sq units 2) 6 sq units 3) 1 sq units 4) 2 sq units Solution: (4) 2 sq units... View Article