List of top Questions asked in CBSE CLASS XII

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 \(x-axis\)

Determine order and degree(if defined)of differential equation \(\frac{d^4y}{dx^4}\)+sin(y''')=0

\(If ƒ(x)=∫_0^xt\ sin\ t\ dt,\ then  ƒ'(x)is\)

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

From the differential equation of the family of hyperbolas having foci on \(x\)-axis and centre at origin.
Find the area of the region bounded by curves \(y=x^2+2,y=x,x=0\) and \(x=3\)
The value of \(∫^1_0tan^{-1}\frac{(2x-1)}{(1+x-x^2)}dx\) is

Find the area bounded by the curve y=sin x between x=0 and x=2π

If \(ƒ(a+b-x)=ƒ(x)\),then \(∫^b_axƒ(x)dx\) is equal to
\(∫\frac{cos2x}{(sinx+cosx)^2}dx\) is equal to

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

Evaluate \(∫^1_0e^{2-3x}dx\) as a limit of a sum.

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