Find the area of the smaller region bounded by the ellipse \(\frac{x^2}{9}\)+\(\frac{y^2}{4}\)=1 and the line
\(\frac{x}{3}\)+\(\frac{y}{2}\)=1
Find the area enclosed by the parabola 4y=3x2 and the line 2y=3x+12
Find the area enclosed between the parabola y2=4ax and the line y=mx
Find the area bounded by the curve y=sin x between x=0 and x=2π
Find the area of the region lying in the first quadrant and bounded by y=4x2,x=0,y =1 and y=4
Find the area between the curves y=x and y=x2
Find the area under the given curves and given lines:
(i)y=x2,x=1,x=2 and x-axis
(ii)y=x4,x=1,x=5 and x-axis
Area lying between the curve y2=4x and y=2x is
Smaller area enclosed by the circle x2+y2=4 and the line x+y=2 is
Using integration find the area of the triangular region whose sides have the equations y =2x+1,y=3x+1 and x=4.
Using integration finds the area of the region bounded by the triangle whose vertices are (–1, 0),(1, 3)and(3, 2).
\(\int \frac{dx}{\sin^2 x \cos^2 x}\) equals
Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related?
Show that each of the relation R in the set A = { x ∈ Z : 0 ≤ x ≤ 12}, given by I. R={(a,b):Ia-bI is a multiple of 4} II. R={(a,b):a=b}is an equivalence relation. Find the set of all elements related to 1 in each case.