class 12

Math

Calculus

Application of Integrals

The area enclosed by the curves$y=sinx+cosxandy=∣cosx−sinx∣$ over the interval $[0,2π ]$

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Find the area of the parabola $y_{2}=4ax$bounded by its latus rectum.

Find the area of the region bounded by the curve $y_{2}=x$and the lines $x=1,x=4$and the x-axis.

The area bounded by the curve $y=x∣x∣$, x-axis and the ordinates $x=−1$and $x=1$is given by(A) 0 (B) $31 $ (C) $32 $ (D) $34 $[Hint : $y=x_{2}$if $x>0$and $y=−x_{2}$if $x<0$].

Sketch the region lying in the first quadrant and bounded by $y=4x_{2}$, $x=0$, $y=2$ and $y=4$. Find the area of the region using integration.

Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).

Find the area of the region ${(x,y):0≤y≤x_{2}+1,0≤y≤x+1,0≤x≤2}$

Find the area lying above x-axis and included between the circle $x_{2}+y_{2}=8x$and the parabola $y_{2}=4x$.

Find the area bounded by the curve $x_{2}=4y$and the line $x=4y_{2}$.