List of top Mathematics Questions on applications of integrals asked in CBSE CLASS XII

Find the area of the circle 4x2+4y2=9 which is interior to the parabola x2=4y
Area bounded by the curve y=x3, the x-axis and the ordinates x=2 and x=1 is
Find the area bounded by curves(x-1)2+y2=1 and x2+y2=1
Area of the region bounded by the curve y2=4x, y-axis and the line y=3 is
Area lying in the first quadrant and bounded by the circle x2+y2=4 and the lines x=0 and x=2 is
Find the area of the region bounded by the curve y2=4x and the line x=3
Find the area bounded by the curve x2=4y and the line x=4y-2

Sketch the graph of y=|x+3|and evaluate \(\int_{-6}^{0} |x+3| \,dx\)

Find the area of the region bounded by the ellipse \(\frac{x2}{4}+\frac{y^2}{9}=1\)
Using the method of integration find the area of the region bounded by lines:
\(2x+y=4,3x–2y=6\) and \(x–3y+5=0\)
Using the method of integration find the area of the triangle ABC,coordinates of whose vertices are A(2,0),B(4,5)and C(6,3)
Find the area bounded by curves{\((x,y):y≥x^2\) and \(y=|x|\)}

Find the area of the smaller region bounded by the ellipse \(\frac{x^2}{a^2}\)+\(\frac{y^2}{b^2}\)=1 and the line \(\frac{x}{a}\)+\(\frac{y}{b}\)=1

Using the method of integration find the area bounded by the curve\(|x|+|y|=1\)
[Hint:the required region is bounded by lines \(x+y=1,x–y=1,–x+y=1\) and \(–x–y=11\)]
Find the area of the region enclosed by the parabola \(x^2=y\),the line \(y=x+2\) and \(x-axis\)
The area bounded by the \(y-axis,y=cosx\) and \(y=sinx\) when \(0≤x≤\frac{π}{2}\)
The area of the circle \(x^2+y^2=16\) exterior to the parabola \(y^2=6x\) is

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

The area bounded by the curve \(y=x|x|\),\(x\)-axis and the ordinates \(x=–1\) and \(x=1\) is given by
[Hint:\(y=x^2\, if\, x>0\) and \(y=–x^2\) if \(x<0]\)
Find the area of the region\({(x,y):y^2≤4x,4x^2+4y^2≤9}\)

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 of the region bounded by curves \(y=x^2+2,y=x,x=0\) and \(x=3\)

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