Class 12

Math

Calculus

Application of Integrals

Using integration, find the area of the region bounded by the line $2y=−x+8$,x-axis is and the lines $x=2$ and $x=4$.

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Find the area of the region bounded by the parabola $y=x_{2}$ and $y=∣x∣$.

Find the area bounded by the curve $y=cosx$between $x=0$and $x=2π$.

The area of the figure bounded by the parabola $(y−2)_{2}=x−1,$ the tangent to it at the point with the ordinate y=3, and the x-axis is

Find the area of the region enclosed by the curves $y=xgxandy=2x−2x_{2}˙$

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

If $A_{n}$ is the area bounded by $y=xandy=x_{n},n∈N,thenA_{2}A˙_{3}A_{n}=$ $n(n+1)1 $ (b) $2_{∩}(n+1)1 $ $2_{n−1}n(n+1)1 $ (d) $2_{n−2}n(n+1)1 $

For which of the following values of $m$ is the area of the regions bounded by the curve $y=x−x_{2}$ and the line $y=mx$ equal $29 ?$ (a) $−4$ (b) $−2$ (c) 2 (d) 4

Area lying in the first quadrant and bounded by the circle $x_{2}+y_{2}=4$ and the lines \displaystyle{x}={0}{\quad\text{and}\quad}{x}={2}<{l}{a}{t}{e}{x}> is(A) \displaystyle\frac{<}{{l}}{a}{t}{e}{x}>\pi<{l}{a}{t}{e}{x}> (B) \displaystyle\frac{<}{{l}}{a}{t}{e}{x}>\frac{\pi}{{2}}<{l}{a}{t}{e}{x}> (C) \displaystyle\frac{<}{{l}}{a}{t}{e}{x}>\frac{\pi}{{3}}<{l}{a}{t}{e}{x}> (D) \displaystyle\frac{<}{{l}}{a}{t}{e}{x}>\frac{\pi}{{4}}