Class 12

Math

Calculus

Area

The parabolas $y_{2}=4xandx_{2}=4y$ divide the square region bounded by the lines x=4, y=4 and the coordinate axes. If $S_{1},S_{2},S_{3}$ are the areas of these parts numbered from top to bottom, respectively, then

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

The ratio in which the line $x−1=0$ divides the area bounded by the curves $2x+1=4y+1 ,y=xandy=2$ is

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x-axis, and the ordinates $x=4π andx=β>4π isβsinβ+4π cosβ+2 β.$ Then $f_{′}(2π )$ is

If the area bounded by $f(x)=tanx ,y=f(c),x=0andx=a,0<c<a<2π $ is minimum then find the value of c.

Consider the regions $A={(x,y)∣x_{2}+y_{2}≤100}andB=∣∣ x y ∣∣ sin(x+y)>0}$ in the plane. Then the area of the region $A∩B$ is

Suppose $y=f(x)andy=g(x)$ are two functions whose graphs intersect at the three point (0, 4), (2,2) and (4, 0) with f(x) gt g(x) for 0 lt x lt 2 and f(x) lt g(x) for 2 lt x lt 4. If $∫_{0}[f(x)−g(x)]dx=10and∫_{2}[g(x)−f(x)]dx=5$, the area between two curves for 0 lt x lt 2, is

$Givenf(x)=0∫ x e_{t}(g_{e}sect−sec_{2}t)dt,g(x)=−2e_{x}tanx,$ then the area bounded by the curves $y=f(x)andy=g(x)$ between the ordinates $x=0andx=3π ,$ is (in sq. units)

$Two curvesC_{1}≡[f(y)]_{2/3}+[f(x)]_{1/3}=0andC_{2}≡[f(y)]_{2/3}+[f(x)]_{2/3}=12,satisfying the relation(x−y)f(x+y)−(x+y)f(x−y)=4xy(x_{2}−y_{2})$ The area bounded by the curve $C_{2}and∣x∣+∣y∣=12 $ is

The area (in sq. units) of the region ${(x,y):y_{2}≥2xandx_{2}+y_{2}≤4x,x≤0,y≥0}$ is