Class 12

Math

Calculus

Area

The area between the curve $y=2x_{4}−x_{2}$, the x-axis, and the ordinates of the two minima of the curve is

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Sketch the curves and identify the region bounded by $x=21 ,x=2,y=Inx,andy=2_{x}.$ Find the area of this region.

If $S_{0},S_{1},S_{2},…$ are areas bounded by the x-axis and half-wave of the curve $y=sinπx ,then prove thatS_{0},S_{1},S_{2},…$ are in A.P…

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

Consider two curves $C_{1}:y=x1 andC_{2}:y=$ In x on the xy plane. Let $D_{1}$ denotes the region surrounded by $C_{1},C_{2},$ and the line x=1 and $D_{2}$ denotes the region surrounded by $C_{1},C_{2}and the line x=a. IfD_{1}=D_{2},$ then the sum of logarithm of possible values of a is ___.

Area of the region bounded by the curve $y=tanx$ and lines y = 0 and x = 1 is

Let $f:[0,∞)→R$ be a continuous function such that $f(x)=1−2x+0∫ x e_{x−t}f(t)dtfor allx∈[0,∞).$ Then, which of the following statements(s) is (are)) TRUE?

The area enclosed between the curve $y_{2}(2a−x)=x_{3}$ and the line x=2 above the x-axis is

The area of region(s) enclosed by the curve $y=x_{2}$ and $y=∣x∣ $ is