Class 12

Math

Calculus

Application of Integrals

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

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Find the area under the given curves and given lines:(i) $y=x_{2},$$x=1,x=2$and x-axis(ii) $y=x_{4}$, $x=1,x=5$and x-axis

Find the area bounded by the curve $y=(x−1)(x−2)(x−3)$ lying between the ordinates $x=0andx=3.$

Sketch the curves and identity the region bounded by $x=21 ,x=2,y=1nx,andy=2_{x}˙$ Find the area of this region.

Find the area bounded by the parabola $y=x_{2}+1$ and the straight line $x+y=3.$

Let $f(x)$=M a xi mu m${x_{2},(1−x)_{2},2x(1−x)},$ where $0≤x≤1.$ Determine the area of the region bounded by the curves $y=f(x)$,x-axis ,x=0,\displaystyle{\quad\text{and}\quad}<{l}{a}{t}{e}{x}>x=1.\displaystyle\frac{<}{{l}}{a}{t}{e}{x}>

Find the area of the figure enclosed by the curve $5x_{2}+6xy+2y_{2}+7x+6y+6=0.$

Find the area of the region in the first quadrant enclosed by the x-axis, the line $y=x$, and the circle $x_{2}+y_{2}=32$.

Find the area bounded by the curves $x_{2}+y_{2}=4,x_{2}=−2 y$ and $x=y$