PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the area bounded by the parabola y² = 4x and the line y = 2x − 4 By using horizontal strips.

If the area above the x-axis, bounded by the curves y = 2^kx and x = 0, and x = 2 is \[\frac{3}{\log_e 2}\], then the value of k is __________ .

The area included between the parabolas y² = 4x and x² = 4y is (in square units)

The area bounded by the curve y = log_e x and x-axis and the straight line x = e is ___________ .

The area bounded by y = 2 − x² and x + y = 0 is _________ .

The area bounded by the parabola x = 4 − y² and y-axis, in square units, is ____________ .

If A_n be the area bounded by the curve y = (tan x)ⁿ and the lines x = 0, y = 0 and x = π/4, then for x > 2

The area of the region formed by x² + y² − 6x − 4y + 12 ≤ 0, y ≤ x and x ≤ 5/2 is ______ .

The area of the region bounded by the parabola (y − 2)² = x − 1, the tangent to it at the point with the ordinate 3 and the x-axis is _________ .

The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is _____________ .

The area bounded by the parabola y² = 4ax and x² = 4ay is ___________ .

The area bounded by the curve y = x⁴ − 2x³ + x² + 3 with x-axis and ordinates corresponding to the minima of y is _________ .

The area bounded by the parabola y² = 4ax, latusrectum and x-axis is ___________ .

The area of the region \[\left\{ \left( x, y \right) : x^2 + y^2 \leq 1 \leq x + y \right\}\] is __________ .

The closed area made by the parabola y = 2x² and y = x² + 4 is __________ .

The area of the region bounded by the parabola y = x² + 1 and the straight line x + y = 3 is given by

The ratio of the areas between the curves y = cos x and y = cos 2x and x-axis from x = 0 to x = π/3 is ________ .

Area bounded by parabola y² = x and straight line 2y = x is _________ .

The area bounded by the curve y = 4x − x² and the x-axis is __________ .