Related InterviewSolutions

• Evaluate:  \(\int\limits_0^1\cfrac{tan^{-1}}{(1+x^2)}dx\)∫ tan-1x/(1+x2)dx, x ∈[0,1]
• Evaluate:  \(\int\limits_2^43dx\)∫ 3dx, x ∈[2,4]
• The area of the region enclosed by the curve y = 1/x , and the lines x = e, x = e2 is given by(a) 1 sq unit (b) 1/2 sq units (c) 3/2 sq units (d) 5/2 sq units
• The area bounded by the region 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by (a) 12 sq units (b) 8 sq units (c) 25 sq units (d) 32 sq units
• The area of the region bounded between the line x = 4 and the parabola y2 = 16x is(a) 128/3 sq units (b) 108/3 sq units (c) 118/3 sq units (d) 218/3 sq units
• The area of the region included between the parabolas y2 = 4ax and x2 = 4ay, (a > 0) is given by(a) 16a2/3 sq units (b) 8a2/3 sq units (c) 4a2/3 sq units (d) 32a2/3 sq units
• The area of the circle x2 + y2 = 25 in first quadrant is (a) 25π/3 sq units (b) 5π sq units (c) 5 sq units (d) 3 sq units
• The area bounded by the curve y = tan x, X-axis and the line x = π/4 is(a) 1/3 log 2 sq units (b) log 2 sq units (c) 2 log 2 sq units (d) 3 log 2 sq units
• The area of the region bounded by x2 = 16y, y = 1, y = 4 and x = 0 in the first quadrant, is(a) 7/3 sq units (b) 8/3 sq units (c) 64/3 sq units (d) 56/3 sq units
• The area bounded by the ellipse and the line \(\cfrac{x^2}{a^2}+\cfrac{y^2}{b^2} = 1\) x2/a2 + y2/b2 = 1 is(a) πab – 2ab sq units (b) πab/4 - ab/2  sq units (c) (πab – ab) sq units (d) πab sq units